United States v. Thomas Addaquay

Opinion

NOT FOR PUBLICATION

In the

United States Court of Appeals For the Eleventh Circuit

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No. 25-10609

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UNITED STATES OF AMERICA, Plaintiff-Appellee,

versus

THOMAS ADDAQUAY, Defendant-Appellant.

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Appeals from the United States District Court for the Northern District of Georgia D.C. Docket No. 1:20-cr-00126-LMM-JSA-1

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No. 25-10611

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UNITED STATES OF AMERICA, Plaintiff-Appellee,

versus

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THOMAS ADDAQUAY, Defendant-Appellant.

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Appeals from the United States District Court for the Northern District of Georgia D.C. Docket No. 1:23-cr-00290-LMM-1

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Before JORDAN, ROSENBAUM, and LAGOA, Circuit Judges. PER CURIAM:

Thomas Addaquay controlled a business called United Consolidated Accounting and Business Services. On paper, United Consolidated was a check-cashing business. But the government presented evidence that it served a different function: turning refund checks generated by fraudulent tax returns into money that Addaquay and others could use. A jury convicted Addaquay of wire fraud, aggravated identity theft, and related offenses. And Addaquay later pled guilty in a separate case to structuring transactions to evade federal reporting requirements. The district court sentenced him in both cases together.

In these consolidated appeals, Addaquay challenges several of his convictions and the resulting loss and restitution calculations. He also argues that the government violated Brady v. Maryland, 373 U.S. 83 (1963), and Giglio v. United States, 405 U.S. 150 (1972), by failing to disclose four investigative memoranda before trial and that the district court should have compelled additional discovery.

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After careful consideration, we affirm.

I. Background

A. The Criminal Proceedings This appeal arises from two criminal cases that the district court resolved together at a consolidated sentencing.

In 2020, the government first charged Thomas Addaquay with fraud offenses in Case No. 1:20-cr-45 (“fraud case”). While that case was pending, the government indicted Addaquay in Case No. 1:20-cr-126 (“tax-refund-fraud case”). That second indictment alleged a sprawling scheme involving stolen personal information, fraudulent federal income-tax returns, and the processing of the resulting refund checks.

The tax-refund-fraud indictment charged Addaquay with one count of conspiracy to commit wire fraud, in violation of 18 U.S.C. § 1349; ten counts of wire fraud, in violation of 18 U.S.C. § 1343; five counts of aggravated identity theft, in violation of 18 U.S.C. § 1028A(a)(1); one count of conspiracy to commit money laundering, in violation of 18 U.S.C. § 1956(h); and twelve counts of money laundering, in violation of 18 U.S.C. § 1957. As relevant here, the government alleged that Addaquay and others used United Consolidated Accounting and Business Services, which the parties called “UC,” to turn fraudulently obtained tax refunds into money they could use. At trial, the jury found Addaquay guilty on all twenty-nine counts.

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Addaquay later pled guilty in a third case, Case No. 1:23-cr-

290 (“structuring case”), to structuring transactions to evade federal reporting requirements, in violation of 31 U.S.C. §§ 5324(a)(1) and (d). As part of his plea agreement, the government dismissed the indictment in the fraud case. The district court eventually sentenced Addaquay in the tax-refund-fraud and structuring cases together .

B. How the Tax-Refund Scheme Worked We begin by explaining how the tax-refund-fraud scheme worked. 1 The scheme had three basic parts. First, participants obtained taxpayers’ personal identifying information, or “PII,” including names, dates of birth, addresses, and Social Security numbers. Second, tax preparers used that information to file federal income- tax returns without the taxpayers’ permission. Those returns generated tax refunds, often in the form of refund-anticipation-loan checks issued through private financial institutions. We refer to those instruments as “refund checks.” Third, the participants needed a way to cash those checks without the presence of the taxpayers named on them.

1 We present the evidence in the light most favorable to the verdict for the

government. See United States v. Jiminez, 564 F.3d 1280, 1284 (11th Cir. 2009) (citing United States v. Williams, 144 F.3d 1397, 1401 (11th Cir. 1998)).

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That is where UC came in. Addaquay controlled UC and presented it as a legitimate check-cashing business. From November 2012 through June 2015, UC used a company called ReliaFund as its third-party payment processor. UC scanned checks and transmitted them to ReliaFund in batches. ReliaFund then deposited the checks through its processing bank and electronically transferred the proceeds, minus fees, to UC. During their relationship, ReliaFund processed approximately $13 million in deposits submitted by UC.

At trial, the government asserted that this arrangement allowed the participants to turn fraudulent returns into spendable money. Addaquay offered a different account. He maintained that UC was a legitimate business that specialized in cashing third-party tax-refund checks brought in by tax preparers.

C. The Evidence at Trial The government used several categories of evidence to support its account.

1. Kevin Edwards’s Testimony Kevin Edwards described the scheme from the inside. He testified that, beginning around 2010 or 2011, he helped Addaquay cash refund checks. Edwards deposited the checks, retained 30% of the proceeds, and returned the balance to Addaquay. Addaquay then distributed the money among the participants.

Edwards also connected Addaquay to the preparation side of the scheme. According to Edwards, Addaquay paid people to

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obtain folders containing taxpayers’ personal information and brought that information to his Lenox Road office. Edwards testified that Michael Awiti prepared fraudulent returns using that information . He recalled Addaquay referring to Awiti as his partner, although Edwards admitted that he did not know whether Awiti was Addaquay’s partner or employee. Edwards sometimes delivered proceeds directly to Awiti and, on approximately two occasions , gave Awiti cashier’s checks representing his share.

Edwards’s direct dealings with Addaquay ended around 2012. According to Edwards, their relationship ended after Addaquay developed other banking relationships and began using UC to perform the check-cashing function that Edwards had previously performed.

Addaquay’s counsel vigorously cross-examined Edwards.

Edwards admitted that he participated in the fraud, kept part of the proceeds, and received immunity. Counsel also elicited that Edwards ’s relationship with Addaquay ended badly after Edwards believed that Addaquay had cut him out of the operation.

2. Addaquay’s Possession of Taxpayers’ Information Other evidence connected Addaquay to taxpayers’ personal information. Elizabeth Washington testified that Addaquay gave her files containing customers’ names, addresses, and Social Security numbers. He instructed her to enter that information into a spreadsheet and check the status of the customers’ tax refunds.

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The government also introduced emails containing names, Social Security numbers, dates of birth, and tax-preparation instructions . One email from Nana Addaquay included instructions for preparing returns using Drake tax-preparation software. An investigating agent later found suspicious returns filed in the names of people identified in the emails. Those same names appeared on refund checks that UC submitted through ReliaFund.

3. UC’s Actual Operations The people who worked at UC described a business that looked different from the ordinary check-cashing operation Addaquay claimed to run.

Simon Wedderburn worked for Addaquay and later at UC’s Marietta storefront. He saw some customers but little ordinary check-cashing activity. Addaquay instead sent Wedderburn checks to verify using telephone numbers and verification codes printed on them.

Amar Medjedovic gave a similar account. Addaquay hired him to work at the check-cashing business, verify and deposit checks, and withdraw money from an account that Medjedovic had opened. Medjedovic understood that Addaquay obtained the checks through relationships with tax preparers or accounting firms.

Sacoya Lyons testified about another unusual feature of the operation. On two occasions, Addaquay directed her to sign taxpayers ’ names on refund checks. Lyons then scanned the endorsed

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checks at Addaquay’s office. She also saw another woman signing names on checks there.

Other evidence reinforced that testimony. About 99% of the more than 4,000 checks UC submitted through ReliaFund were related to tax refunds. Most were issued through private tax-refund companies or financial institutions rather than directly by the United States Department of the Treasury.

ReliaFund eventually warned Addaquay that some checks had been returned as unauthorized or fraudulent. Still, only about 48 of the more than 4,000 checks UC submitted were returned as bad. ReliaFund’s representative also acknowledged that check cashing is a high-risk business in which some fraudulent checks may pass through an otherwise-legitimate operation.

4. The Taxpayers and Tax Preparer Numbers The government also called taxpayers whose names appeared on returns and refund checks processed through UC. Those taxpayers testified that they had not authorized the returns, did not know the listed preparers, and had not received the resulting refunds .

Some returns listed a preparer tax identification number.

The Internal Revenue Service (“IRS”) assigns that number to a person who prepares federal tax returns for compensation. Several witnesses whose identities had been used to obtain preparer tax identification numbers testified that they had never applied for such a number and had never worked as tax preparers.

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The trial evidence did not directly connect Addaquay to every fraudulently obtained preparer tax identification number. But it allowed the jury to trace particular unauthorized returns and their resulting refund checks through the UC and ReliaFund processing system.

D. The Challenged Counts The wire-fraud counts Addaquay challenges on appeal involved two kinds of electronic transmissions.

Counts 2 through 5 and Count 7 charged electronic transfers from ReliaFund to a UC bank account. Each transfer represented the proceeds of a batch of checks UC had submitted for processing. For each charged batch, the government identified at least one refund check generated by a tax return that the named taxpayer had not authorized.

Counts 8 through 11 charged the electronic filing of unauthorized 2014 tax returns. Each return used a real taxpayer’s name and Social Security number and generated a refund check. Records showed that UC later submitted each resulting check through Relia Fund and received the proceeds.

Counts 13 through 16 charged aggravated identity theft based on the taxpayers’ identities used in the returns underlying Counts 8 through 11. The government’s theory was that Addaquay knowingly helped a scheme that used real taxpayers’ identities to file unauthorized returns and then processed the resulting checks through UC.

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Each of the challenged counts also charged Addaquay with aiding and abetting the offenses under 18 U.S.C. § 2.

The jury found Addaquay guilty on each count. E. Post-Trial Disclosures and Motions Shortly before Addaquay’s originally scheduled sentencing, the government produced four memoranda prepared during separate investigations. One summarized an interview with Michael Awiti. The other three summarized two interviews and a proffer involving Gianna Liady.

1. The Awiti Memorandum Awiti told investigators that he began using stolen identities to prepare fraudulent tax returns in 2010. He identified several sources of the stolen information, none of whom was Addaquay. Awiti used Drake tax-preparation software, multiple names, electronic filing identification numbers, and private companies to generate the resulting refund checks.

Awiti also described his dealings with Addaquay and Edwards . He said Addaquay knew that Awiti’s refund checks resulted from returns filed using stolen identities. When Awiti needed someone to cash those checks, Addaquay introduced him to Edwards . According to Awiti, Addaquay attended the beginning of their meeting but then moved away while Awiti and Edwards negotiated their own arrangement. Edwards would cash Awiti’s

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checks, keep 40% of the proceeds, and return the rest to Awiti. Addaquay was not present for their later exchanges and, in Awiti’s words, “only made the introduction.”

Awiti also described separate fraudulent dealings with Addaquay . He said Addaquay helped him convert fraudulent proceeds into cashier’s checks, used the names of his businesses as remitters to make the money appear legitimate, and charged between 8% and 15% for that service. Awiti further stated that Addaquay cashed fraudulent refund checks for him and other tax preparers .

2. The Liady Documents Liady admitted preparing false returns through K1 Financial.

She described fraudulent practices associated with K1 Financial and Point 1, including the use of stolen identities. She also identified others involved in preparing fraudulent returns and provided investigators with a spreadsheet listing electronic filing identification numbers, companies, and individuals associated with Point 1.

The documents did not identify Addaquay as a participant in Liady’s tax-preparation scheme. Addaquay maintained that they supported his defense because they showed that tax preparers could independently generate fraudulent refunds whose checks a business like UC might later process.

3. The Motions for a New Trial and Additional Discovery Based on the Awiti memorandum and the Liady documents, Addaquay moved to dismiss the indictment or for a new trial under

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Brady v. Maryland, 373 U.S. 83 (1963), and Giglio v. United States, 405 U.S. 150 (1972). He argued that Awiti’s account contradicted Edwards ’s testimony and that the Liady documents supported his defense that independent tax preparers generated fraudulent returns without his direction or knowledge. He also produced checks or account records reflecting transactions involving K1 Financial, Point 1, and others.

The district court denied the motion. Among other things, it concluded that evidence of Liady’s separate tax-preparation scheme did not exculpate Addaquay from knowingly processing fraudulent checks through UC.

Addaquay also moved to compel additional materials concerning Awiti, Edwards, Liady, K1 Financial, Point 1, and others. He sought investigative records, the tax returns associated with checks UC had processed, information identifying the preparers of those returns, and K1 Financial’s client list.

The district court distinguished among Addaquay’s requests . It ordered the government to produce the responsive tax returns already in its possession because those returns could bear directly on the loss calculation. But it denied the broader requests for investigative files and K1 Financial’s client list because Addaquay had not connected those materials to any particular loss included in the government’s calculation.

F. Loss and Restitution The presentence investigation report (“PSR”) initially attributed $13,785,093.67 in loss to Addaquay. That figure effectively

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treated all, or nearly all, of the tax-refund checks UC processed through ReliaFund as fraudulent. It resulted in a twenty-level increase under the United States Sentencing Guidelines.

Addaquay objected. He argued that the government had not proved that every UC refund check was fraudulent or attributable to him. He also challenged the government’s sampling method, its reliance on IRS Transaction Code 841 as an indicator of fraud, and its use of the mean rather than the median to extrapolate the loss.

The district court shared some of those concerns. At a June 2024 hearing, it distinguished the jury’s verdict from a finding that every check UC processed was fraudulent. It also questioned whether the government’s relatively small sample justified an extrapolation across approximately 4,198 checks. The court directed the government to provide additional explanation of its methodology when calculating loss to develop the sentencing record further.

At sentencing, the government presented two methods for estimating loss attributable to Addaquay’s scheme. The first rested on the government’s position that fraud permeated UC’s tax-refund business and estimated loss based on all tax-refund checks processed through the business during the relevant period.

Anticipating the district court might prefer a more conservative methodology, the government also offered an alternative estimate based on sampling and extrapolation. IRS Agent Robert Stevens began with approximately 4,198 checks that UC submitted to ReliaFund and excluded 74 checks that were not associated with

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tax refunds as well as 104 other checks that had previously been investigated. He then analyzed a random sample of 300 refund checks and reviewed IRS records associated with those transactions .

Of the sampled checks, 157 corresponded to accounts containing Transaction Code 841, which reflected efforts by the IRS to freeze or reverse refund payments. Using the average loss associated with those checks and assigning zero loss to checks without Transaction Code 841, the government extrapolated an alternative loss estimate of approximately $8 million.

Addaquay responded with an expert statistician, Jeffrey Martin . Martin testified that an unusually large transaction distorted the government’s use of the mean. He also identified an error in which one item selected for the sample incorporated the value of four checks. Using the median instead, which he argued is a better measure of central tendency, Martin calculated a loss of $5,497,966.07.

The district court credited those criticisms. It declined to treat all the tax-refund checks processed through UC as fraudulent and adopted Martin’s lower, median-based calculation. The court then reduced that figure by another 25% “in the abundance of caution ” to account for potentially legitimate checks, the limitations of Transaction Code 841, and fraud not shown to be attributable to Addaquay. That produced a final loss and restitution amount of $4,123,474.55 and an eighteen-level increase under the United States Sentencing Guidelines.

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G. The Judgment and Appeals The district court imposed concurrent sentences of 126 months on Counts 1 through 11 in the tax-refund-fraud case and 120 months on Counts 17 through 29 in that case and on the structuring count in the structuring case. It also imposed concurrent 24- month sentences on Counts 12 through 16, to run consecutively to the sentences on the remaining counts. Addaquay’s total sentence was therefore 150 months’ imprisonment.

The district court imposed two restitution awards. In the tax-refund-fraud case, it ordered Addaquay to pay $4,123,474.55 to the IRS, jointly and severally with Nana Addaquay and Sacoya Lyons . In the structuring case, it ordered him to pay $3,635,861.97 to the identified victims. Addaquay challenges the first award here, not the separate restitution award imposed in the structuring case.

Addaquay timely appealed both judgments, and we consolidated the appeals. He now challenges the sufficiency of the evidence supporting several wire-fraud and aggravated-identity-theft convictions, the government’s post-trial disclosures, the denial of his motions to compel, and the district court’s loss and restitution calculation.

II. Discussion

Addaquay makes four arguments on appeal. First, Addaquay asserts that the evidence was insufficient to support his convictions on Counts 2–5 and 7–11, for wire fraud, and Counts 13–16, for aggravated identity theft in the tax-refund-fraud case. Second, Addaquay argues that the district court erred by finding no

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Brady/Giglio violation had occurred. Third, he contends that the district court abused its discretion by denying his motion to compel the government to produce evidence relevant to the Brady/Giglio inquiry. And fourth, Addaquay says the district court erred in determining the amount of loss and restitution. We consider each argument in turn.

A. The evidence is sufficient to support convictions on all appealed counts. Addaquay argues that the evidence was insufficient to support his convictions on Counts 2–5 and 7–11 for wire fraud, and Counts 13–16, for aggravated identity theft, in the tax-refund-fraud case. As we’ve noted, these counts are also charged under an aiding -and-abetting theory, under 18 U.S.C. § 2. Addaquay’s arguments separately target the wire-fraud counts and the aggravated- identity-theft counts.

i. The Wire-fraud Challenge As to wire fraud, Addaquay’s sufficiency challenge contains three parts. First, Addaquay argues that the government failed to present evidence that the specific wire transfers were part of the “scheme or artifice to defraud” alleged in the indictment or that Addaquay filed or directed the filing of the underlying fraudulent returns. Second, Addaquay asserts that the government improperly assumed that all checks UC sent to ReliaFund were fraudulent and that Addaquay perpetrated or directed the underlying fraud. Finally, Addaquay contends that the Fifth Circuit case United States v. Ragan, 24 F.3d 657 (5th Cir. 1994), compels a different result.

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In evaluating whether sufficient evidence supports a conviction , we view the evidence in the light most favorable to the prosecution and draw all reasonable inferences and credibility choices in favor of the jury verdict. United States v. Deason, 965 F.3d 1252, 1262 (11th Cir. 2020). And unless no reasonable construction of the evidence supports the jury’s guilty verdict beyond a reasonable doubt, we must affirm a conviction. United States v. Merrill, 513 F.3d 1293, 1299 (11th Cir. 2008).

A conviction for wire fraud under 18 U.S.C. § 1343 requires the government to prove beyond a reasonable doubt that the defendant (1) participated in a scheme or artifice to defraud, (2) did so with intent to defraud, and (3) used, or caused the use of, interstate wire transmissions for the purpose of executing the scheme or artifice to defraud. United States v. Machado, 886 F.3d 1070, 1082–83 (11th Cir. 2018). A jury may infer intent from the defendant’s conduct as well as circumstantial evidence. Id. at 1083.

The indictment also charged Addaquay as an aider or abettor , which describes one who “aids, abets, counsels, commands, induces or procures [a crime’s] commission” or who “willfully causes an act to be done,” and directs that he is guilty as a principal. 18 U.S.C. § 2. To support a conviction for aiding and abetting an offense , the evidence must simply show that “the ‘defendant was associated with the criminal venture, participated in it as something he wished to bring about, and sought by his action to make it succeed .’” United States v. Hewitt, 663 F.2d 1381, 1385 (11th Cir. 1981) (quoting United States v. Martinez, 555 F.2d 1269, 1272 (5th Cir.

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1977)). The evidence need not show that the defendant participated in every phase of the venture. Id.

Together, these principles frame the sufficiency question here. The government did not have to prove that Addaquay personally filed each fraudulent return, personally sent each wire transmission, or participated in every step of the scheme. But it did have to prove more than association with people who committed fraud. It had to present evidence from which a reasonable jury could find that Addaquay knowingly associated himself with the charged fraudulent venture, participated in it as something he wished to bring about, and acted to make it succeed. See United States v. Schwartz, 666 F.2d 461, 463 (11th Cir. 1982). We therefore first consider the evidence connecting Addaquay to the alleged scheme and then ask whether that evidence supports the challenged wire-fraud counts. The record here is sufficient to sustain Addaquay’s wire-fraud convictions.

1. Evidence at trial established the existence and operation of the overarching fraud scheme. The government argued at trial that Addaquay engaged in a fraudulent scheme to obtain the personal information of taxpayers to prepare and file fraudulent tax returns so that he and his coconspirators could get paid the resulting tax refunds. The government presented evidence that Addaquay’s scheme worked in three main steps.

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First, “runners,” individuals with access to personal identifying information from sources such as doctors’ offices, obtained victims ’ personal identifying information, including names, dates of birth, and Social Security numbers. They then sent or hand-delivered that information to Addaquay.

Second, Addaquay’s hired tax preparers used the stolen information to file unauthorized federal tax returns in the victims’ names, generating refund checks.

Finally, Addaquay used the fraudulent checks to get himself paid. Initially, Addaquay directed Edwards to cash the resulting tax-refund checks. In 2012, Addaquay created an account with Relia Fund, a check-cashing and credit-card processing company, where he or his coconspirators would upload the refund checks, ReliaFund would process them, and the money from the refund checks would be deposited into his account. To get ReliaFund to work with him, Addaquay invented a story that he ran a legitimate check-cashing business called United Consolidated and that the business had been booming with three locations and many customers cashing checks. Based on Addaquay’s representations, Relia- Fund allowed Addaquay to process numerous checks on a neardaily basis. ReliaFund then deposited the proceeds into accounts Addaquay controlled.

The jury also heard testimony corroborating Addaquay’s role in the overall scheme. Kevin Edwards described the scheme’s general structure and testified that he observed Addaquay meeting

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with a runner, who supplied the stolen personal identifying information . Edwards also testified that, at times, Addaquay directed him to cash refund checks generated by fraudulent tax returns. After Edwards did so, he returned the cash to Addaquay, minus Edwards ’s fee. Then, Addaquay used the proceeds to pay the runners, preparers, and himself.

Elizabeth Washington, who did administrative work for Addaquay in 2011, said that he provided her with files that contained lists of personal identifying information and told her that it was relevant to his tax-preparation business. But she never saw any customers . Simon Wedderburn, who also worked for Addaquay, similarly testified that he rarely observed customers cashing checks. And Amar Medjedovic, another employee, said that he also “never actually saw a customer come by.”

Besides this evidence, Medjedovic testified that Addaquay regularly instructed employees to open bank accounts, which Addaquay then controlled. Addaquay also instructed them to forge endorsements, and obtain and deliver cashier’s checks at his direction .

Plus, Sacoya Lyons and Benjamin Grover, other employees of Addaquay, testified that Addaquay gave them tax-refund checks and instructed them to forge taxpayer signatures.

This evidence was more than enough to allow a reasonable jury to find that Addaquay knowingly participated in the fraudulent tax-refund scheme and did so with intent to defraud. The evidence, if credited, did not merely place him near fraudulent activity. It

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connected him to the acquisition of stolen personal identifying information , the processing of fraudulent refund checks, the use of UC’s accounts, the forging of taxpayer endorsements, and the distribution of proceeds. That evidence established the broader scheme and Addaquay’s role in it.

2. Evidence at trial established each element of the charged counts of substantive wire fraud. Addaquay argues that insufficient evidence ties him to the charged, substantive wire-fraud counts he challenges. We disagree .

In a substantive mail- or wire-fraud case, the government need not prove the defendant personally mailed the item or aided and abetted the specific mailing as part of the scheme to defraud. United States v. Ward, 486 F.3d 1212, 1222 (11th Cir. 2007) (involving mail fraud). Rather, the government must prove only that one participant in the fraudulent scheme knowingly caused the use of the mails or wires in furtherance of the scheme and that the defendant knowingly participated in the scheme or artifice to defraud. Id. Indeed, in United States v. Watkins, we said that “a defendant may be convicted of [wire] fraud without personally committing each and every element of [wire] fraud, so long as the defendant knowingly and willingly joined the criminal scheme, and a coschemer used the [wires] for the purpose of executing the scheme.” 42 F.4th 1278, 1284 (11th Cir. 2022) (quoting Ward, 486 F.3d at 1222).

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Given the voluminous evidence of Addaquay’s role in the scheme, the remaining task is narrower: to determine whether the specific transmissions charged in Counts 2–5 and 7–11 were uses of the wires in execution of that fraudulent tax-refund scheme. At trial, the government introduced evidence connecting each challenged wire-fraud count to a victim taxpayer, a refund check issued from an unauthorized return, and a ReliaFund transfer depositing the proceeds into UC accounts that the jury could find Addaquay controlled.

Counts 2 through 5 and 7 followed the same pattern, and so we discuss them together. Count 2 charged the March 11, 2015, wire transfer of $53,012.14 from ReliaFund to UC’s BB&T account. ReliaFund records showed a March 11, 2015, settlement to UC in that amount. The related batch included nine refund checks bearing endorsement signatures and a stamp directing “deposit to United Consolidated, Inc. for deposit to ReliaFund, Inc.” Lyons testified that the checks in that exhibit looked like the checks Addaquay asked her to endorse in other people’s names, conduct she understood to be wrong. And A.N., one taxpayer whose refund check was included in the batch, testified that she authorized no one to prepare her 2014 tax return, did not know the listed preparer , had never heard of UC, and did not recall receiving the refund check.

Count 3 charged the March 13, 2015, wire transfer of $34,532.30 from ReliaFund to the same UC account. ReliaFund records showed a March 13, 2015, settlement involving a batch of

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five checks sent from ReliaFund to UC. R.K., one taxpayer whose return was associated with that batch, testified that someone had filed a 2014 tax return in his name without authorization. He also testified that he did not know the listed preparer and that the listed individual had not prepared his and his wife’s jointly filed taxes.

Count 4 charged the March 16, 2015, wire transfer of $26,961 from ReliaFund to UC’s BB&T account. ReliaFund records showed a March 16, 2015, settlement involving a batch of three checks totaling $26,961. B.B., one taxpayer whose refund check was included in that batch, testified that he learned someone had filed a tax return using his Social Security number. The return listed a preparer he did not use, and he had never heard of UC.

Count 5 charged the March 17, 2015, wire transfer of $17,619.35 from ReliaFund to UC’s BB&T account. ReliaFund records showed a March 17, 2015, settlement in that amount to the account ending in 3566. The related batch included three checks, including one issued in A.J.’s name. A.J. testified that the tax return filed in her name listed her Social Security number and identified a preparer whom she had not authorized to prepare her taxes.

Count 7 charged the March 19, 2015, wire transfer of $18,213.30 from ReliaFund to UC’s BB&T account. ReliaFund records showed a March 18, 2015, settlement in that amount to the account ending in 3566. 2 The related batch included four checks,

2 The indictment alleged that this settlement occurred on or about March 19,

2015, while the ReliaFund records reflect a date of March 18, 2015. This oneday discrepancy presents no issue. United States v. Reed, 887 F.2d 1398, 1403

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including one issued in L.B.’s name. L.B. testified that the tax return filed in her name listed her and her daughter’s Social Security number and she authorized no one to file a tax return on her behalf.

Taken together, the taxpayer testimony and ReliaFund records allowed the jury to find that the charged transmissions were part of the fraudulent tax-refund scheme. Each charged settlement included at least one refund check generated by an unauthorized return, was processed through the UC-ReliaFund arrangement, and was deposited into a UC account that the jury could find Addaquay controlled. That evidence was sufficient to establish that Counts 2 through 5 and 7 were uses of the wires in execution of the fraudulent tax-refund scheme.

Counts 8 through 11 involved the electronic filing of fraudulent 2014 tax returns. Those counts focused on an earlier step of the same scheme: the filing of unauthorized returns using stolen personal identifying information to generate refund checks. Count 8 illustrates the pattern with the filing-side counts. It charged the March 20, 2015, electronic filing of a 2014 tax return in J.H.’s name. J.H. testified that he later discovered a fraudulent return had been filed in his name; the return contained his Social Security number, but he had never worked with the listed preparer, Dan John.

(11th Cir. 1989) (“When the government charges that an offense occurred ‘on or about’ a certain date, the defendant is on notice that the charge is not limited to the specific date or dates set out in the indictment. Proof of a date reasonably near the specified date is sufficient.”) (internal citation omitted).

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The government also provided other evidence connecting the return to stolen preparer information: D.W. testified that her Social Security number appeared on a preparer tax identification number report, and the same preparer tax identification number appeared on J.H.’s return under the name Dan John, even though D.W. had never prepared taxes and had never worked with J.H.

And beyond the filing, the evidence showed that the unauthorized return generated a refund check, and that the check was then processed through ReliaFund and ultimately deposited into a UC account. That evidence connected the charged electronic filing to the same payment-processing channel the government identified as the final step of Addaquay’s scheme.

Counts 9 through 11 followed the same pattern. Each count charged the electronic filing of an unauthorized 2014 return in a taxpayer’s name: R.M. for Count 9, T.S. for Count 10, and E.B. and G.B. for Count 11. Each taxpayer testified that the return filed in his or her name was unauthorized and that the taxpayer did not receive the resulting refund. And for each count, records showed that the unauthorized return generated a refund check that was processed through ReliaFund and ultimately deposited into a UC account. That evidence allowed the jury to find that Counts 9 through 11, like Count 8, were not isolated false filings but filings that generated refund checks and fed directly into the UC accounts at the center of the scheme. Thus, sufficient evidence established that Counts 8 through 11 were uses of the wires in execution of the fraudulent tax-refund scheme that Addaquay participated in.

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3. The government did not have to prove that every check UC sent to ReliaFund was fraudulent. Addaquay argues that the government improperly assumed that all checks UC sent to ReliaFund were fraudulent and that he was the one who directed or perpetrated any underlying fraud. That argument mistakes the government’s burden on the substantive wire-fraud counts. The government was not required to prove that every check UC processed was fraudulent or attributable to Addaquay. Rather, it had to present sufficient evidence only that the particular transmissions charged in the indictment were used to execute the scheme that Addaquay knowingly joined. See United States v. Williams, 527 F.3d 1235, 1241 (11th Cir. 2008).

The government met that burden. Start with the charged settlements themselves. Each settlement included at least one refund check that taxpayer testimony established resulted from an unauthorized return. And each settlement followed the same path: UC submitted the checks to ReliaFund, ReliaFund processed them, and the proceeds landed in a UC account that Addaquay controlled. So the government did not ask the jury to infer fraud merely because UC’s name appeared somewhere in the transaction. Rather, the government introduced evidence of fraud within each charged settlement and traced the settlement through the payment channel that Addaquay established and controlled.

The evidence about UC’s operations supplied additional context. Addaquay told ReliaFund that UC was a thriving check- cashing business with three locations and many customers. But the

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people who worked for him described something very different. They saw little or no customer check-cashing activity. And approximately 99% of the more than 4,000 checks UC submitted to Relia- Fund were tax-refund-related. That’s an unusual mix for the general check-cashing business Addaquay claimed to operate. More telling still, employees testified that Addaquay gave them tax-refund checks to verify and deposit and instructed them to sign the taxpayers’ names on those checks.

The jury was entitled to put those pieces together. It could reasonably infer that the fraudulent refund check from each charged settlement was not an accidental bad check that happened to pass through an otherwise-legitimate business. Additionally, the jury could reasonably infer the charged settlement used the UC- ReliaFund arrangement to convert fraudulently obtained refund checks into money deposited in an account Addaquay controlled.

4. United States v. Ragan, 24 F.3d 657 (5th Cir. 1994), doesn’t compel a different result. Third, and finally, Addaquay relies on the Fifth Circuit’s decision in United States v. Ragan, 24 F.3d 657 (5th Cir. 1994). Of course, Ragan is an out-of-circuit precedent, so it doesn’t bind us. See Bonner v. City of Prichard, 661 F.2d 1206, 1209 (11th Cir. 1981) (en banc) (“Under the established federal legal system the decisions of one circuit are not binding on other circuits.”). But even as persuasive authority, Ragan does not help Addaquay because it involved a different record and a different theory of liability.

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Ragan concerned fictitious securities trades designed to generate commissions for the defendant. Id. at 658. But the government ’s witness connected Ragan to only trades that were not charged in the indictment. Id. at 660. No evidence connected him to the particular trade tickets underlying his mail- and wire-fraud convictions. Id. So the Fifth Circuit reversed: proof that Ragan participated in some fictitious trades did not show that he participated in the charged ones.

That’s not the case here. As we’ve explained, the government connected each charged transmission to an unauthorized return and traced the resulting refund through UC and ReliaFund into an account Addaquay controlled. And Addaquay was charged as an aider and abettor. So the government did not have to prove that Addaquay personally filed each return or sent each wire. Rather , it had to prove that he knowingly helped the scheme succeed and that the charged wires executed that scheme. The evidence permitted the jury to find both. Thus, Ragan does not help Addaquay .

ii. The Aggravated-identity-theft Challenge Addaquay also challenges his convictions on Counts 13 through 16 for aggravated identity theft. Each of those counts corresponds to one of the electronic-filing wire-fraud counts we have discussed: Count 13 to the return filed in J.H.’s name in Count 8, Count 14 to R.M.’s return in Count 9, Count 15 to T.S.’s return in Count 10, and Count 16 to E.B. and G.B.’s return in Count 11.

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To prove aggravated identity theft, the government had to establish that, during and in relation to wire fraud, Addaquay, or someone he aided and abetted, knowingly used, without lawful authority , a means of identification belonging to another person. See 18 U.S.C. §§ 2, 1028A(a)(1), (c)(5); United States v. Barrington, 648 F.3d 1178, 1192 (11th Cir. 2011). An aider and abettor must intend to facilitate the commission of the offense. Rosemond v. United States, 572 U.S. 65, 76 (2014).

Addaquay makes two arguments directed at the sufficiency of the aggravated-identity-theft charges. First, in line with the arguments he made about his wire-fraud convictions, Addaquay similarly argues that no evidence showed that he, or any of his associates , used the means of identification that the specific counts charged. Second, relying on Rosemond, Addaquay asserts that the government failed to prove that he knew in advance that another participant would use real persons’ identities without lawful authority .

1. Evidence presented at trial specifically established the elements of the charged aggravated-identity-theft counts.

The evidence supporting Counts 8 through 11 rebuts Addaquay ’s first argument. In fact, the evidence reflected that each charged return used a real taxpayer’s name and Social Security number without authorization. It also showed that each return then generated a refund check that was processed through Relia- Fund and deposited into a UC account Addaquay controlled. In other words, the government did not rely merely on evidence that

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Addaquay participated in similar identity theft elsewhere. Rather, it connected each identity charged in Counts 13 through 16 to a particular unauthorized return and traced the resulting refund through the scheme’s payment channel. That evidence permitted the jury to find that a participant in the scheme knowingly used each victim’s identity without lawful authority during and in relation to wire fraud.

2. Rosemond v. United States does not compel a different result . Addaquay asserts that Rosemond v. United States, 572 U.S. 65 (2014), requires vacatur of his aggravated-identity-theft convictions . We disagree.

Rosemond explains that an aider and abettor must intend to facilitate the “specific and entire crime charged.” Id. at 76. And because a person cannot intentionally assist a crime that he learns about only after it is complete, the defendant must have had the required knowledge while he could still choose whether to participate . See id. at 77–78. Relying on that principle, Addaquay argues that evidence that the refunds eventually reached his accounts does not establish that he knew in advance about the identity thefts charged in Counts 13 through 16.

But the evidence did more than trace the refunds to Addaquay after the identities had been used. Recall how the scheme worked. Runners supplied stolen personal identifying information, including taxpayers’ names, dates of birth, and Social Security numbers . Preparers used that information to file unauthorized returns.

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And the resulting refund checks were processed through UC and ReliaFund.

The evidence placed Addaquay within that process from beginning to end. Edwards saw Addaquay meet with a runner who supplied stolen personal identifying information. Washington testified that Addaquay gave her files containing taxpayers’ identifying information. And Lyons and Grover testified that Addaquay instructed them to sign taxpayers’ names on the resulting refund checks. So the jury could infer that Addaquay knew about the identity theft while he was still helping the scheme succeed, not only after the resulting money reached his accounts.

Nor did the government rely on just Addaquay’s use of other, uncharged identities. As we have explained, each identity charged in Counts 13 through 16 appeared on a particular unauthorized return, and the resulting refund check traveled through the UC-ReliaFund channel Addaquay controlled. The evidence therefore connected the charged identities to the same identity- theft process that the jury concluded Addaquay knowingly helped carry out.

iii. Addaquay’s sufficiency challenge fails.

At bottom, Addaquay asks us to view each piece of evidence in isolation. He emphasizes that no witness saw him file the specific returns charged in the indictment, that UC may have processed some legitimate checks, and that the proceeds reached his accounts only after the victims’ identities had been used. The jury heard that account and rejected it. It was entitled to do so.

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The evidence showed that Addaquay received taxpayers’

personal identifying information, worked with runners and preparers , directed employees to forge endorsements on tax-refund checks, established the UC-ReliaFund channel through which those checks were processed, and controlled the accounts that received the proceeds. And for each challenged count, the government connected a specific unauthorized return or refund check to that same channel. Viewed as a whole and in the light most favorable to the verdict, that evidence permitted a reasonable jury to find that Addaquay knowingly helped execute the charged wire frauds and aggravated identity thefts. We therefore affirm Addaquay ’s convictions on the challenged Counts 2 through 5, 7 through 11, and 13 through 16.

ii. The district court properly denied Addaquay ’s motion for a new trial because a Brady/Giglio violation did not occur.

Addaquay argues that the government violated Brady v. Maryland , 373 U.S. 83 (1963), and Giglio v. United States, 405 U.S. 150 (1972), by failing to disclose four investigative documents before trial. As we’ve mentioned, one memorandum summarized investigators ’ interview with Michael Awiti, an alleged coconspirator in Addaquay’s scheme. The other three documents summarized two interviews and a proffer involving Gianna Liady, who participated in a separate tax-fraud scheme.

We review an alleged Brady-Giglio violation de novo and the denial of a motion to dismiss an indictment and a motion for a new

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trial for an abuse of discretion. United States v. Jordan, 316 F.3d 1215, 1248–49 (11th Cir. 2003) (motion to dismiss); United States v. Gallardo , 977 F.3d 1126, 1142 n.12 (11th Cir. 2020) (motion for a new trial).

The Supreme Court and we have recognized that, “regardless of request, favorable, exculpatory or impeachment evidence is material, and constitutional error results from its suppression by the government, if there is a reasonable probability that, had the evidence been disclosed to the defense, the result of the proceeding would have been different.” United States v. Noriega, 117 F.3d 1206, 1218 (11th Cir. 1997) (quoting Kyles v. Whitley, 514 U.S. 419, 433 (1995)) (internal citations, brackets, and quotation marks omitted). To establish a Brady violation, Addaquay must show all four of the following circumstances:

(1) the government possessed favorable evidence to the defendant; (2) the defendant does not possess the evidence and could not obtain the evidence with any reasonable diligence; (3) the prosecution suppressed the favorable evidence; and (4) had the evidence been disclosed to the defendant, there is a reasonable probability that the outcome would have been different.

United States v. Vallejo, 297 F.3d 1154, 1164 (11th Cir. 2002). A reasonable probability is one sufficient to undermine confidence in the verdict. Kyles, 514 U.S. at 434. When the government withholds multiple items, we consider their cumulative effect. Id. at 436–37.

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“Giglio error, a species of Brady error, occurs when the undisclosed evidence demonstrates that the prosecution’s case included perjured testimony and that the prosecution knew, or should have known, of the perjury.” Ford v. Hall, 546 F.3d 1326, 1331 (11th Cir. 2008) (internal quotation marks omitted). “To prevail on a Giglio claim, a [defendant] must establish that (1) the prosecutor knowingly used perjured testimony or failed to correct what he subsequently learned was false testimony; and (2) such use was material i.e., that there is any reasonable likelihood that the false testimony could have affected the judgment.” Id. at 1331–32 (internal quotation marks and ellipses omitted).

Addaquay cannot make the necessary showing here. Even assuming the government suppressed favorable evidence, the Awiti memorandum does not create a reasonable probability of a different verdict. Nor does it establish that Edwards testified falsely. And the Liady documents concerned an unrelated tax- fraud operation and did not undermine the evidence connecting Addaquay to the charged conduct. We address the Awiti memorandum first, then turn briefly to the Liady documents before considering the documents’ cumulative effect.

i. The Awiti memorandum. Addaquay advances both a Brady claim and a Giglio claim based on the Awiti memorandum. Under his Brady theory, the memorandum would have allowed him to show that Awiti and Edwards conducted their own criminal operation, contrary to Edwards ’s testimony placing Addaquay at the center of the scheme.

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Addaquay’s Giglio theory is that this asserted conflict established that Edwards testified falsely and that the government failed to correct his testimony.

The district court concluded that the memorandum was not sufficiently material to undermine confidence in the verdict. We agree. For purposes of Addaquay’s Brady claim, we assume that the government suppressed favorable evidence and ask whether there is a reasonable probability that timely disclosure would have produced a different result. Addaquay’s Giglio claim presents the separate threshold question whether the memorandum establishes that Edwards actually testified falsely.

1. Edwards’s Testimony At trial, Edwards described his involvement with Addaquay ’s scheme, which began sometime in 2010. From approximately 2010 through the end of 2012, Edwards played a key role in cashing the refund checks, after which he provided the proceeds to Addaquay. As Edwards described, Addaquay would supply Edwards with refund checks resulting from fraudulent tax returns. Next, Edwards would deposit the checks into “multiple” bank accounts that he controlled. Under his agreement with Addaquay, Edwards retained 30% of the proceeds from the checks. Once the funds became available for withdrawal, sometimes that occurred the same day of the deposit, Edwards would procure them in the form of cash or cashier checks and then give the money to Addaquay . Edwards then testified that Addaquay would distribute

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the proceeds to other participants in the scheme, including preparers and runners, while keeping some of the money for himself.

Although other witnesses described pieces of Addaquay’s scheme, Edwards connected those pieces and added detail to the inner workings of the scheme. Edwards noted that tax season was a particularly busy time for Addaquay and his scheme participants. He described the operation as involving about five checks per day. Before depositing the checks, Edwards and other scheme participants would call the bank to verify them. The banks would provide a verification number that allowed the deposit of refund checks into Edwards’s bank accounts.

Throughout his recounting, Edwards testified to Addaquay ’s knowledge of the fraudulent scheme. Edwards said he became more directly involved with the scheme when he overheard a phone call between Addaquay and another individual, in which Addaquay discussed difficulties he was having getting “reliable people” to cash the refund checks. To address this problem, Edwards said he would step in to cash the checks for a fee.

On several occasions, Edwards traveled with Addaquay to locations where Addaquay would pick up personal identifying information from runners. For instance, Edwards observed Addaquay meeting with a woman dressed in scrubs. When Addaquay returned to the car after receiving personal identifying information, Addaquay told Edwards that the woman worked at a doctor’s office . Addaquay later explained to Edwards that the personal identifying information he received from the runners was necessary to

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process refund checks. Edwards testified that Addaquay and other participants knew the checks were unauthorized because frequent issues arose from stop-payment orders after taxpayers reported unauthorized use of the information.

Edwards also testified about his observation and dealings with Michael Awiti, who is the subject of the investigatory memo at the heart of Addaquay’s Brady and Giglio claims. In this respect, Edwards said he did not know whether Awiti was a business partner or a direct employee in the scheme. But Edwards recalled that Addaquay considered Awiti a partner and that he prepared tax returns . Edwards also testified that rather than bringing the cash directly to Addaquay, sometimes he would give the cash from the refund checks to Awiti instead. On about two occasions, Edwards gave Awiti a cashier’s check that represented Awiti’s share for his role in the scheme. Thus, Edwards did not deny dealing with Awiti, and he expressly acknowledged uncertainty about Awiti’s precise relationship with Addaquay.

Edwards’s dealings with Addaquay ended in late 2012. He said that happened because Addaquay began establishing his own relationship with banks and other means of check-cashing, so Addaquay no longer needed to rely on Edwards. Edwards also became more fearful of criminal liability when the Secret Service came to his residence to investigate certain fraudulent IRS checks that had come from Addaquay.

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As Edwards saw things, Addaquay invented UC as a front to perform the check-cashing functions Edwards had previously performed . Edwards was not happy that Addaquay had gone behind his back and cut him out of the operation.

Edwards faced a vigorous cross-examination. He admitted that he participated in the fraud, retained 30% of the proceeds, and, for his testimony, received immunity from prosecution as it related to the Addaquay scheme. Defense counsel also elicited that Edwards ’s relationship with Addaquay ended badly after Edwards believed that Addaquay had cut him out of the operation. Drawing on that testimony, counsel portrayed Edwards as a criminal participant with reasons to minimize his own role, shift responsibility to Addaquay, and testify favorably for the government. Counsel ultimately suggested that Edwards, not Addaquay, was the scheme’s mastermind.

2. Awiti’s Account The investigatory memo reported that Awiti admitted he prepared fraudulent tax returns beginning in 2010. So the memo identified the interview’s purpose as obtaining further information about the stolen identity and tax-refund fraud case involving Addaquay , Edwards, Awiti, and others.

Awiti said that Addaquay introduced him to Edwards so that Edwards could cash the refund checks generated by Awiti’s fraudulent returns. At their first meeting, Addaquay drove with Awiti to a restaurant, where Addaquay introduced Awiti and Edwards. Addaquay moved to another table so that Awiti and Edwards could

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discuss matters privately. From there, Awiti said he and Edwards entered into a direct arrangement, where Edwards deposited Awiti’s fraudulent refund checks. Edwards retained 40% of the proceeds, and Edwards returned the remainder to Awiti. Addaquay did not participate in these later handoffs because, according to Awiti, Addaquay “only made the introduction and was no longer involved” in those later transactions between Awiti and Edwards .

As for his separate dealings with Addaquay, Awiti also told investigators that Addaquay knew the refund checks were generated from returns filed using stolen identities. After receiving proceeds from Edwards, Awiti worked with Addaquay to convert the funds into cashier’s checks. Addaquay placed the name of his business in the remitter section to make the funds appear more legitimate . Awiti said that Addaquay charged between 8% and 15% for the service. According to Awiti, Addaquay conducted five or six such transactions, generally involving $20,000 to $30,000, between 2011 and 2013. Awiti further said that Addaquay independently cashed fraudulent refund checks for him, and Addaquay cashed fraudulent refund checks for other tax preparers who filed returns using stolen identities.

So Awiti’s account cut in two directions. It gave Addaquay a basis to argue that Edwards minimized his independent relationship with Awiti. But it also separately incriminated Addaquay for knowingly cashing and disguising proceeds from returns filed using stolen identities.

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3. The Awiti memorandum was not material. Awiti’s memorandum was not material for four primary reasons . First, Awiti’s account did not contradict Edwards’s central testimony. Second, the jury already knew the principal reasons to distrust Edwards. Third, Awiti’s account cut both ways: although it supplied additional (cumulative) impeachment of Edwards, it also implicated Addaquay in fraudulent conduct. Fourth, independent evidence corroborated Addaquay’s knowledge and participation .

Principally, Awiti’s account is not material because it did not contradict Edwards’s central testimony. Edwards testified from firsthand knowledge about his own arrangement with Addaquay. According to Edwards, he cashed refund checks for Addaquay and retained 30% of the proceeds. Awiti described a separate arrangement under which Edwards cashed Awiti’s refund checks and retained 40%. And Awiti said that Addaquay separately helped him cash or convert fraudulent proceeds. These arrangements could have existed at the same time.

Nothing in Awiti’s account contradicted Edwards’s testimony about his direct dealings with Addaquay. Awiti did not say that Edwards never cashed fraudulent checks for Addaquay, that Addaquay never supplied Edwards with those checks, or that Addaquay did not knowingly participate in refund fraud. To the contrary , Awiti said that Addaquay knowingly cashed and disguised fraudulent proceeds for him and other tax preparers.

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And Edwards never testified that every transaction involving Awiti ran through Addaquay. Edwards acknowledged that he sometimes delivered proceeds directly to Awiti, and he admitted that he did not know whether Awiti was Addaquay’s partner or employee. So the memorandum would have allowed Addaquay to challenge Edwards’s description of the participants’ precise relationships . But it did not undermine Edwards’s central firsthand testimony that he cashed fraudulent refund checks directly for Addaquay .

Second, the jury already knew the principal reasons to distrust Edwards. Edwards admitted that he participated in the fraudulent -refund scheme and retained 30% of the proceeds from the checks he deposited for Addaquay. The jury also knew that Edwards had received immunity. And defense counsel cross-examined him extensively about his criminal conduct, the money he received , his incentive to cooperate with the government, and his strained relationship with Addaquay. Drawing on that testimony, counsel portrayed Edwards as the scheme’s mastermind who minimized his own role and shifted responsibility to Addaquay.

The Awiti memorandum would have given counsel a more specific example to support that argument. But it would not have revealed a previously unknown source of bias or reason for Edwards to testify falsely. The jury already assessed Edwards’s credibility knowing that he was a paid participant in the scheme, was protected from prosecution, was cooperating with the govern-

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ment, and had reasons to minimize his own culpability. Any additional impeachment value was therefore limited. See United States v. Jones, 601 F.3d 1247, 1266–67 (11th Cir. 2010) (concluding that the nondisclosure of impeachment evidence was harmless when the evidence did not contradict the witness’s testimony and the jury already knew that the witness hoped to receive a reduced sentence for cooperating).

Third, Awiti’s account implicated Addaquay in fraudulent conduct, limiting the memorandum’s value to the defense. Awiti told investigators that Addaquay knew the refund checks resulted from returns filed using stolen identities. He also described Addaquay ’s repeated help to disguise the proceeds. According to Awiti, Addaquay used his businesses’ names as remitters to make the funds appear legitimate and charged between 8% and 15% to do that. Awiti further stated that Addaquay cashed fraudulent refund checks for him and other tax preparers over several years.

Addaquay responds that Awiti did not connect him to the particular offenses charged here. And to be sure, Awiti did not identify the specific 2015 transmissions underlying the challenged counts. But Awiti’s account showed Addaquay knowingly facilitated fraudulent-refund activity. So it contradicted Addaquay’s proposed use of the memorandum to portray himself as an innocent check casher who did not know that the checks resulted from fraud.

Fourth, substantial evidence independent of Edwards’s testimony established Addaquay’s knowledge and participation.

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Washington testified that Addaquay gave her files containing taxpayers ’ personal information. Emails also showed Nana Addaquay sent Addaquay personal information and detailed instructions concerning tax filings. And Lyons and Grover testified that Addaquay gave them refund checks and instructed them to sign the taxpayers’ names. Victims, in turn, confirmed that they had not authorized the returns or resulting checks.

The evidence concerning UC told the same story. Addaquay directed employees to open the accounts through which checks payable to other people were processed. Although Addaquay portrayed UC as a legitimate check-cashing business, employees saw few or no customers, and its storefronts were rarely open. Yet UC submitted more than 4,000 checks to ReliaFund, approximately 99% of which were tax-refund related, and received more than $12 million in proceeds. Those proceeds flowed into accounts that Addaquay controlled, and an auditor traced some of the money to his personal expenditures, including a luxury vehicle.

Finally, Edwards’s direct participation ended around 2012, while the charged UC transactions occurred later. Edwards explained that Addaquay developed UC to replace the check-cashing function Edwards had previously performed. ReliaFund records, employee testimony, and victim testimony independently established Addaquay’s later conduct. Nothing in the Awiti memorandum undermined that evidence. So even if the memorandum had weakened parts of Edwards’s testimony, the remaining evidence strongly supported the jury’s verdict.

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4. Addaquay’s criticisms of the district court’s analysis don’t change the result. Addaquay’s criticisms of the district court do not change the result. He first argues that the district court asked only whether Edwards’s testimony and Awiti’s account could coexist. True, Brady materiality does not turn on whether a court can imagine some way to reconcile two accounts. The question is whether there is a reasonable probability that disclosure would have produced a different result. But the degree of conflict between the accounts can matter to that inquiry.

Here, though, Awiti’s account did not conflict with Edwards ’s firsthand testimony about his dealings with Addaquay. It merely supplied additional details about Edwards’s separate dealings with Awiti.

Addaquay next argues that the district court improperly relied on the memorandum’s inculpatory contents. But a court cannot evaluate favorable statements in a vacuum. It must consider how the defense could have used them and what that use would have revealed to the jury. Had Addaquay used the memorandum to show that Edwards minimized his relationship with Awiti, the jury also would have learned that Awiti accused Addaquay of knowingly cashing and disguising fraudulent proceeds. Those statements affected the helpfulness of the proposed impeachment.

Finally, Addaquay emphasizes that Awiti did not connect him to the specific crimes charged. That is true. But the government presented other evidence tying the charged transactions to

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UC and Addaquay. And the memorandum did not undermine that evidence. In the end, the memorandum would have sharpened Addaquay’s attack on Edwards, but it would not have placed the government’s case in a materially different light. In short, there’s no reasonable probability that the memorandum’s disclosure would have produced a different verdict.

5. Addaquay’s Giglio claims fail as well. Addaquay’s Giglio theory also fails. Giglio requires false testimony , not merely testimony that another witness could have impeached or supplemented. United States v. Michael, 17 F.3d 1383, 1385 (11th Cir. 1994). And Addaquay falls short there.

Addaquay identifies several parts of Edwards’s testimony that he says were false. In Addaquay’s view, Edwards falsely portrayed Awiti as Addaquay’s partner or employee, falsely testified that Awiti prepared fraudulent returns at Addaquay’s direction using personal information that Addaquay supplied, and falsely suggested that Addaquay controlled the proceeds paid to Awiti. Addaquay also asserts that Edwards falsely implied that he dealt with Awiti only through Addaquay. The Awiti memorandum, Addaquay argues, tells a different story: Awiti prepared fraudulent returns independently and maintained his own check-cashing arrangement with Edwards. But a closer comparison of the two accounts reveals no such contradiction.

The memorandum did not establish that Edwards testified falsely. Start with Awiti’s relationship to Addaquay. Edwards did

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not claim to know whether Awiti was Addaquay’s partner or employee . To the contrary, he expressly admitted that he did not know which description was accurate. And the fact that Awiti maintained an independent arrangement with Edwards does not mean that Awiti had no separate relationship with Addaquay or never prepared returns for him. Both relationships could have existed .

The memorandum also did not contradict Edwards’s testimony about the source of Awiti’s personal information. Awiti did not say that Addaquay never supplied him with personal information . Rather, the memorandum simply did not address that point. Silence on a subject is not the same as a contrary account.

Nor did the memorandum contradict Edwards’s testimony about the proceeds. Edwards acknowledged at trial that he sometimes delivered proceeds directly to Awiti. The memorandum added details about those transactions, including the percentage Edwards retained and Addaquay’s absence from later handoffs. But additional details do not make Edwards’s testimony false.

At most, the memorandum showed that Edwards’s account was incomplete and that he may not have understood the precise relationship between Awiti and Addaquay. But Giglio requires more. A fuller account from another participant does not establish that the trial testimony was false.

And because Addaquay has not shown that Edwards testified falsely, we need not consider whether the prosecution knew of any falsity.

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Even if we assume that some part of Edwards’s testimony was false and that the government knew it, Addaquay’s Giglio claim still fails. The alleged falsehood concerned the precise relationship among Edwards, Awiti, and Addaquay. It did not undermine Edwards ’s firsthand account of his own dealings with Addaquay. Nor did it undermine the evidence that Addaquay possessed taxpayers’ personal information, directed employees to endorse checks in taxpayers ’ names, controlled UC’s operations, and participated in the charged transactions. And the memorandum itself described Addaquay knowingly cashing and disguising fraudulent proceeds. So there’s no reasonable likelihood that a fuller description of Edwards ’s relationship with Awiti would have affected the jury’s verdict .

ii. The Liady Documents As for the Liady documents, Addaquay argues that Liady’s separate fraud showed how tax preparers could independently falsify returns and generate fraudulent refund checks without involving the businesses that later processed those checks. From that premise, he reasons that UC may likewise have processed fraudulent checks without his knowledge.

That theory is too attenuated to establish materiality. The Liady documents described a separate tax-preparation operation. Although other evidence reflected some financial dealings between UC and entities associated with Liady, K1, or Point 1, that evidence did not connect Liady’s fraudulent activity to the charged victims, the charged transmissions, or any particular refund check that UC

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processed. We first describe the Liady documents and Addaquay’s proposed use, and then we explain why that use does not create a reasonable probability of a different verdict.

The Liady documents described how Liady prepared returns for actual clients through K1 and Point 1, falsified Schedule C information , and thereby increased the clients’ refunds. They did not mention Addaquay or UC.

Addaquay asserts that Liady’s conduct showed that a tax preparer could generate fraudulent refund checks without the knowledge or direction of the business that later processed them. He reasons that UC likewise may have processed fraudulent checks without knowing how they were generated and that he therefore did not necessarily supply personal information or direct the preparers .

But the Liady documents establish only the first step in that reasoning: Liady independently committed tax fraud. They do not show that Liady prepared any of the returns charged in Addaquay’s case, that any check generated by her fraud passed through UC, or that Addaquay unknowingly processed such a check. The rest of Addaquay’s theory depends on facts the documents do not supply.

Not only that, but the documents do not undermine the evidence of Addaquay’s knowing participation. The government presented evidence that Addaquay possessed taxpayers’ personal information , worked with runners and preparers, directed employees to sign taxpayers’ names on refund checks, and controlled the UC accounts that received the proceeds. It also presented evidence

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that UC processed thousands of tax-refund checks despite having few customers and rarely opened storefronts. Nothing in the Liady documents calls that evidence into question.

In sum, the Liady documents may have shown that a tax preparer could commit fraud independently. But they did not show that the preparers involved here operated independently of Addaquay or that he unknowingly processed the charged checks. So no reasonable probability exists that disclosure of the documents would have produced a different verdict.

iii. The cumulative effect of the undisclosed documents does not create a reasonable probability of a different outcome or undermine confidence in the verdict.

Finally, Brady requires us to consider the undisclosed evidence collectively. Kyles, 514 U.S. at 436. Addaquay argues that the Awiti and Liady documents together would have supported a unified defense: tax preparers independently generated fraudulent returns, Edwards independently cashed some of the checks, and Addaquay merely operated a business that processed checks without knowledge of the underlying fraud. We disagree.

As we’ve explained, the Awiti memorandum would have provided some additional impeachment of Edwards, but it also described Addaquay knowingly cashing and disguising fraudulent proceeds. And the Liady documents showed that another tax preparer committed fraud through a separate operation, but they did not connect that operation to the charged conduct here. Putting the documents together does not fill either gap.

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Nor do the documents undermine the other considerable evidence of Addaquay’s guilt, which we’ve already described. Considered separately or together, the undisclosed documents do not place the case in a sufficiently different light to undermine confidence in the verdict. The district court therefore did not abuse its discretion in denying Addaquay’s motion to dismiss or motion for a new trial.

iii. The district court didn’t abuse its discretion when it denied in part Addaquay’s motion to compel.

Addaquay sought three categories of additional discovery.

First, he requested investigative materials concerning Liady, Point 1, K1, Webb, and Wilson. Second, he sought the tax returns underlying checks that UC processed, along with information identifying the preparers and their tax-preparer numbers. Third, he requested K1’s client list.

Addaquay argued that these materials would show that independent tax preparers generated fraudulent returns whose proceeds UC merely cashed. From that premise, he asserted that the materials would serve two purposes. First, he argued, they would undermine his convictions by showing that others, rather than Addaquay , prepared the fraudulent returns. And second, he continued , they would reduce the loss amount by identifying checks generated through schemes in which he did not participate.

The district court concluded that evidence about Liady’s separate tax-preparation scheme did not exculpate Addaquay from

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his role in the charged scheme. But because some of the other requested materials might bear on the loss amount, the court deferred ruling on the motion to compel until sentencing.

The district court ultimately divided the materials into two groups. It denied Addaquay’s requests for investigative materials concerning Liady and the other tax preparers, as well as K1’s client list. As the court reasoned, Addaquay had not connected those materials to any particular loss included in the government’s calculation .

But the court granted in part Addaquay’s request for the tax returns associated with checks UC processed. Because those returns could bear directly on the government’s loss methodology, the court ordered the government to produce the responsive returns then in its possession.

We review the denial of a defendant’s post-trial motion for discovery for abuse of discretion. See United States v. Espinosa-Hernandez , 918 F.2d 911, 913 (11th Cir. 1990). Brady applies after trial only “when it is discovered that the prosecution had material information of which the defense was unaware.” United States v. Arias- Izquierdo, 449 F.3d 1168, 1189 (11th Cir. 2006). Because Brady is not a discovery device, discovery should not be ordered “based upon mere speculation as to whether the material would contain exculpatory evidence. . . .” Id.; see Jordan, 316 F.3d at 1252 n.81 (“[M]ere speculation or allegations that the prosecution possesses exculpatory information will not suffice to prove ‘materiality.’”).

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At sentencing, the government bears the burden of proving, by a preponderance of the evidence, the loss attributable to the defendant . See United States v. Stein, 846 F.3d 1135, 1152 (11th Cir. 2017). But that allocation of the burden did not entitle Addaquay to every investigative document that might conceivably bear on loss. To obtain the materials through a motion to compel, he still had to explain how they were likely to produce information material to the loss calculation.

The district court did not abuse its discretion in its rulings.

To the extent Addaquay sought the materials to challenge his convictions , his request depended on the same premise as his Brady claim: that evidence of fraud committed by Liady and other preparers exculpated him. But as we’ve explained, it did not. Addaquay was convicted not merely of preparing false returns but of knowingly helping process fraudulent refund checks.

To the extent Addaquay sought the materials for sentencing purposes, evidence identifying fraudulent refund checks that Addaquay did not know about or was not deliberately blind to could bear on the loss attributable to him. And Addaquay produced checks showing financial dealings between UC and entities associated with Liady, K1, or Point 1. But those checks did not identify the refund checks underlying the payments, show whether Addaquay knowingly processed them, or establish that any resulting losses fell outside his own conduct or the criminal activity he jointly undertook.

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The district court therefore reasonably distinguished between the requested materials. Addaquay did not identify what he expected the investigative files and K1 client list to contain or connect them to any particular refund check included in the loss calculation . And a mere possibility that further investigation might uncover useful information is not enough to compel broad post-trial discovery. See Arias-Izquierdo, 449 F.3d at 1189.

By contrast, the tax returns associated with checks that UC processed bore directly on the government’s methodology. They could identify the preparer, shed light on whether the taxpayer authorized the return, and test whether the sample reliably supported the government’s inferences about UC’s checks. The district court appropriately ordered the government to produce the responsive returns and associated preparer-identification information then in its possession. Put simply, the district court drew a reasoned line between materials directly capable of testing the proposed loss amount and materials whose relationship to that amount remained speculative.

Addaquay argues that the district court’s discovery ruling improperly required him to prove that he did not conspire with the other preparers. It did not. The court ruled based on whether Addaquay supplied a concrete basis for compelling additional discovery , not whether the government had proved the loss attributable to him. And the government retained that ultimate burden. The court held only that Addaquay had not connected his broader requests to the checks included in the loss calculation, while ordering

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production of the materials that bore directly on the calculation. That was not burden shifting. It was a tailored exercise of the court’s discretion. We therefore affirm the district court’s partial denial of Addaquay’s motion to compel.

iv. The district court didn’t clearly err in determining the loss and restitution amounts and its determinations were supported by the record.

Addaquay challenges the district court’s determination that he was responsible for $4,123,474.55 in loss in the tax-refund-fraud case. He raises three objections. First, he argues that IRS Transaction Code 841 did not reliably establish that a return was fraudulent . Second, he contends that the government failed to show that losses generated by independent tax preparers were attributable to him. Third, he argues that the district court arbitrarily reduced its preliminary estimate by 25%. Based on the same asserted defects, Addaquay also challenges the restitution award in the tax-refund fraud case. Given that the two cases are subject to a combined Guidelines calculation, the calculation of loss in the tax-refund fraud case affects the loss amount applied to the structuring case.

i. Well-established legal principles govern the district court’s loss and restitution determinations.

We review the district court’s factual determination of loss for clear error. United States v. Medina, 485 F.3d 1291, 1304 (11th Cir. 2007). “Although review for clear error is deferential, a finding

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of fact must be supported by substantial evidence.” United States v. Robertson, 493 F.3d 1322, 1330 (11th Cir. 2007).

Section 2B1.1 is the fraud guideline. See U.S.S.G. § 2B1.1.

Under section 2B1.1(a), an offender starts with either six or seven base offense levels depending on the offense. See id. § 2B1.1(a). Then, more levels are added depending on the amount of the loss from the fraud scheme. See id. § 2B1.1(b)(1). Under the commentary to the Guidelines, subject to some exclusions, “[l]oss is the greater of actual loss or intended loss.” Id. § 2B1.1, comment. (n.3(A)). The Guidelines define an “actual loss,” in turn, as a “reasonably foreseeable pecuniary harm that resulted from the offense .” Id. § 2B1.1, comment. (n.3(A)(i)). Intended losses, however , include “the pecuniary harm that the defendant purposely sought to inflict,” including “intended pecuniary harm that would have been impossible or unlikely to occur (e.g., as in a government sting operation, or an insurance fraud in which the claim exceeded the insured value).” Id. § 2B1.1, comment. (n.3(A)(ii)).

When a defendant’s conduct “was permeated with fraud, a district court does not err by treating the amount that was transferred from the victim to the fraudulent enterprise as the starting point for calculating the victim’s pecuniary harm.” United States v. Campbell, 765 F.3d 1291, 1305 (11th Cir. 2014). The government must prove the loss amount by a preponderance of the evidence. United States v. Foley, 508 F.3d 627, 633 (11th Cir. 2007).

Still, “neither this court nor the Guidelines insist that district courts calculate the amount of loss with utmost precision; the

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Guidelines merely require the district court to reach a reasonable estimate of the loss amount. U.S.S.G. § 2B1.1, cmt. n.2(C) [, later redesignated as cmt. n.3(C)]. This is so because the amount of loss is often ‘difficult to determine accurately.’ United States v. Medina, 485 F.3d 1291, 1304 (11th Cir. 2007) (citation and internal quotation marks omitted).” United States v. Bradley, 644 F.3d 1213, 1290 (11th Cir. 2011).

District courts may make loss determinations based on evidence at trial, in addition to evidence at a sentencing hearing. Id. In doing so, a sentencing court need not “constrain itself to absolute figures;” instead, it may “rely on ‘specific circumstantial evidence ’ to estimate the amount of loss.” Id. (quoting United States v. Willis, 560 F.3d 1246, 1251 (11th Cir. 2009)). But while a court can rely on estimates, it “‘must not speculate concerning the existence of a fact which would permit a more severe sentence under the guidelines.’” Id. (quoting United States v. Sepulveda, 115 F.3d 882, 890 (11th Cir. 1997)).

A defendant is responsible for losses resulting from acts that he committed, aided, abetted, or willfully caused. U.S.S.G. § 1B1.3(a)(1)(A). For the acts of others, § 1B1.3(a)(1)(B) requires that those acts fall within the scope of jointly undertaken criminal activity , further that activity, and be reasonably foreseeable in connection with it. See United States v. Presendieu, 880 F.3d 1228, 1245 (11th Cir. 2018); United States v. McCrimmon, 362 F.3d 725, 731 (11th Cir. 2004). Finally, “‘[d]istrict courts are in a unique position to evaluate the evidence relevant to a loss determination,’” so we “must give

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their determinations ‘appropriate deference.’” United States v. Whitman, 887 F.3d 1240, 1248 (11th Cir. 2018) (quoting United States v. Moran, 778 F.3d 942, 973 (11th Cir. 2015)).

ii. How the District Court Proceeded Before sentencing, the district court directed the government to disclose the sources, methodology, and process it intended to use to calculate loss and restitution in the tax-refund-fraud case. In response, the government submitted a written explanation of its methodology.

Given the scale of the fraud at issue here, the government explained that a review of every check or tax document in connection with the scheme would not be feasible and would strain IRS resources. The government permissibly relied on sampling and extrapolation to estimate loss. See, e.g., United States v. Johnson, 841 F.3d 299, 304–05 (5th Cir. 2016) (affirming a tax-loss calculation extrapolated from a sample).

The government began with 4,198 checks that UC submitted to ReliaFund during the relevant period. Although a later review identified 4,334 checks, the government retained the lower figure of 4,198 in Addaquay’s favor. It then separated those checks into three categories. First, it excluded 74 checks that were not readily identifiable as tax-refund checks. Second, it set aside 300 randomly selected checks, which it would use to estimate loss rate among the remaining untested refund checks. Third, it removed 104 checks that investigators had examined separately and whose losses the government would calculate directly. Removing the 300

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sampled checks and the 104 separately examined checks from the extrapolation pool ensured that their losses would not be counted twice. That left 3,720 untested tax-refund checks to which the government would apply the result of its sample.

The government used the 300 randomly selected checks to estimate the loss associated with those 3,720 untested checks. For each check in the sample, Agent Stevens reviewed IRS records to determine how much the government had paid and whether the corresponding taxpayer’s account contained Transaction Code 841. That code reflected an attempt by the IRS to freeze or reverse a refund payment. Still, the code could be entered after a refund check had been cashed.

The government proposed two ways to extrapolate from the sample of 300 checks. Its first approach rested on its position that fraud permeated UC’s business. Under that approach, Stevens added up the IRS payments associated with all 300 sampled refund checks and averaged them, resulting in an average payment of $3,516.62 per check. He applied that average to the 3,720 untested refund checks and then added the losses associated with the sampled and separately examined checks. That calculation produced an estimated loss of $14,623,450.95.

Alternatively, the government offered a more conservative calculation that used Transaction Code 841 as a proxy for fraud. Of the 300 sampled checks, 157 were associated with Transaction Code 841. Those checks corresponded to $563,738.39 in refunds

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that the IRS had actually paid. For purposes of its conservative calculation , Stevens treated the other 143 sampled checks as producing no loss, even though the absence of Transaction Code 841 did not establish that the corresponding returns were legitimate. Agent Stevens likewise assigned zero loss when he could not identify the return associated with a check.

Then Stevens divided the $563,738.39 in confirmed IRS payments by the full 300-check sample, including the 143 checks assigned zero loss. That produced an average loss of approximately $1,879.13 per sampled check. Agent Stevens applied that average to the 3,720 untested refund checks, producing an extrapolated loss of $6,990,356.04. Finally, he added the $563,738.39 associated with the sample and $486,629.30 associated with the checks examined separately. That calculation produced the government’s alternative estimate of $8,040,723.73.

In the government’s view, Transaction Code 841 supplied a conservative proxy because it narrowed the calculation to sampled returns that the IRS had taken action to freeze or reverse. As the government acknowledged, the code did not conclusively establish fraud in every instance. But because the alternative calculation assigned zero loss to every sampled check without the code, any fraudulent return that the code failed to capture lowered rather than increased the estimate.

Addaquay’s expert, Martin, identified two problems with the government’s methodology. First, he explained that the arithmetic mean could be distorted by an unusually large observation,

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while the median would be less affected by such an outlier. Second , one observation in the random sample included the sum of four checks even though only one of those checks had been randomly selected. To limit the effect of those problems, Martin proposed using the median value of the sampled checks rather than the mean. His median-based calculation, which continued to rely on Transaction Code 841, produced an estimated loss of $5,497,966.07.

The district court credited Martin’s criticisms. As the court recognized, the sample was relatively small and Transaction Code 841 was an imperfect proxy: the code could capture some legitimate returns while failing to capture some fraudulent ones. Still, the court found that legitimate transactions represented only a small portion of UC’s activity. Less than two percent of the checks UC submitted to ReliaFund were not tax-refund checks, and the evidence showed little ordinary check-cashing activity at UC’s storefronts. Instead, the court found that Addaquay used UC largely to process the proceeds of his fraud. Based on that evidence, the court found that “a large percentage” of the tax-refund checks UC submitted to ReliaFund were part of the fraud proved at trial.

At the same time, the court explained that it could not find that every check included in Martin’s calculation resulted from fraud attributable to Addaquay. So the court reduced even Martin ’s $5,497,966.07 estimate by 25% “in the abundance of caution.” As the court explained, the reduction reflected the proportion of

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the checks that, in its view, the trial and sentencing evidence sufficiently connected to Addaquay’s fraud. That reduction produced a loss amount of $4,123,474.55. The court used the same figure to calculate restitution in the tax-refund-fraud case.

Addaquay raises three objections to that calculation. First, he argues that Transaction Code 841 did not reliably identify fraudulent returns. Second, he contends that the government failed to establish that losses arising from returns prepared by others were attributable to him. Third, he argues that the district court’s 25% reduction was an arbitrary compromise rather than an estimate grounded in the evidence. We address each argument in turn.

iii. The district court didn’t clearly err in calculating the loss amount.

1. The limitation to Transaction Code 841 did not invalidate the estimate. Addaquay correctly observes that Code 841 did not conclusively establish fraud. Indeed, Agent Stevens acknowledged that the code signified a frozen payment and that the IRS could freeze a payment for nonfraudulent reasons. He also admitted that the code did not necessarily establish identity theft and that he could not explain why the IRS applied it to each particular return.

But the district court did not treat Transaction Code 841 as a fraud label. It expressly recognized that some transactions bearing the code might be legitimate and that some fraudulent transactions might not bear the code. So the court instead treated the code

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as one indicator of fraud within a larger record. That record included taxpayer interviews confirming unauthorized returns, returns associated with fraudulently obtained preparer tax identification numbers, checks established as fraudulent during the original investigation, and the extensive trial evidence concerning UC’s operations .

The uncertainty surrounding some taxpayers did not establish that their returns were legitimate. It meant only that the court could not determine the status of every transaction. And the court did not ignore that uncertainty. It accepted the lower, median- based estimate proposed by Addaquay’s expert and then reduced that figure by another 25% to account in part for Transaction Code 841’s limitations and the possibility of legitimate checks. And the court explained that it used that percentage based on its view of the evidence presented at trial and at sentencing. That approach produced a reasonable estimate rather than a speculative one.

2. Evidence supported attributing the loss to Addaquay. Addaquay emphasizes that the government did not prove that he personally prepared every fraudulent return. But the government didn’t have to. After all, the fraud did not end when a preparer filed a false return. The scheme produced money only when someone cashed the resulting refund check. And the evidence supported the district court’s finding that Addaquay knowingly controlled that part of the operation through UC.

Losses from checks that Addaquay knowingly processed were therefore attributable to him as relevant conduct. See

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U.S.S.G. § 1B1.3(a)(1)(A). It makes no difference for that purpose whether K1, Liady, Point 1, or another preparer filed the underlying return. If a preparer brought a fraudulent refund check to UC and Addaquay knowingly helped process it, his conduct furthered the fraud even if he never touched the return itself.

The evidence supported that finding of knowledge. Tax preparers delivered checks in batches without the named payees present . Checks repeatedly bore forged endorsements. Nearly every check UC submitted to ReliaFund was tax-refund related, even though UC conducted little ordinary check-cashing business. And ReliaFund warned Addaquay about checks reported as unauthorized or fraudulent. From those facts, the district court could reasonably infer that Addaquay knew UC was turning fraudulent returns into money.

3. The 25% reduction was a conservative credit rather than an arbitrary compromise. As for the loss amount, the district court did not simply choose a number between the parties’ competing estimates. It made a series of adjustments tied to problems identified in the evidence . First, it rejected the government’s initial position attributing approximately $14.6 million in losses to Addaquay. Next, it rejected the government’s $8.04 million mean-based extrapolation because an unusually large transaction distorted the mean and one sampled observation improperly included four checks. The court instead adopted Martin’s lower, median-based estimate of $5,497,966.07. It then reduced that figure by another 25%. The

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final estimate was less than one-third of the loss initially attributed to Addaquay.

The court also explained the reason for the additional reduction . After hearing the evidence at trial and sentencing, the court sought to account for legitimate checks, uncertainty surrounding Transaction Code 841, and fraud that may not have been attributable to Addaquay. That distinguishes this case from United States v. Gupta, 572 F.3d 878, 889 (11th Cir. 2009), where the selected figure lacked an articulated evidentiary basis. Here, the district court identified its starting point, corrected a known statistical distortion, and explained the remaining uncertainties that warranted a further discount.

To be sure, the record did not establish that exactly 25% of the estimate represented legitimate or unrelated transactions. But the Guidelines require a reasonable estimate, not mathematical precision. The question is whether the final estimate was plausible in light of the record as a whole. Given the pervasive fraud at UC, the court’s use of the defense-favorable median, and its additional 25% reduction, it was.

iv. The district court correctly calculated and imposed restitution.

Addaquay challenges the $4,123,474.55 restitution award based on the same objections he raises to the district court’s loss calculation. Although Guidelines loss and restitution are distinct, restitution may reflect only the victim’s actual loss caused by the defendant’s conduct. United States v. Baldwin, 774 F.3d 711, 728

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(11th Cir. 2014). Still, when actual loss cannot be calculated precisely , the district court may adopt a reasonable estimate supported by the evidence. Id.; United States v. Moss, 34 F.4th 1176, 1193 (11th Cir. 2022).

The district court’s methodology estimated actual loss to the IRS: refunds that the IRS paid and that UC processed through Relia Fund. The court then adopted Martin’s lower median-based calculation and reduced it by another 25% to account for legitimate or insufficiently attributable transactions. For the reasons we’ve explained, that estimate was supported by the record. Because Addaquay identifies no separate defect in the restitution calculation, the district court did not clearly err in ordering restitution to the IRS in the same amount.

Addaquay does not independently challenge the separate $3,635,861.97 restitution award imposed in the structuring case. We therefore leave it undisturbed.

III. Conclusion

For the foregoing reasons, we affirm Addaquay’s convictions and sentences.

AFFIRMED.