SUMMARY ORDER
UPON DUE CONSIDERATION, IT IS HEREBY ORDERED, ADJUDGED AND DECREED that the judgment of the district court be AFFIRMED.
Mulk Raj Dass and Chloe Peterson appeal from judgments entered in the United States District Court for the Eastern District of New York (Amon, J.) convicting them, after a jury trial, of one count of conspiracy to pay a kickback, in violation of 18 U.S.C. § 371, one count of conspiracy to commit wire fraud, also in violation of § 371, two counts of substantive wire fraud, in violation of 18 U.S.C. § 1343, and two counts of money laundering, in violation of 18 U.S.C. § 1956. All of the charges arose out of defendants’ sale of a phony $10 million investment to an employee benefit pension fund, resulting in a $9.3 million loss to the fund.
On appeal, both defendants contend that their convictions were not supported by sufficient evidence and that the government constructively amended the wire fraud conspiracy count at trial.
1. Sufficiency of Evidence
“When reviewing a conviction for an alleged insufficiency of evidence, this Court will view the evidence in the light most favorable to the government, construe all permissible inferences in its favor, resolve all issues of credibility in favor of the *78jury’s verdict, and uphold a conviction if any rational trier of fact could have found the essential elements of the charged crime beyond a reasonable doubt.” United States v. Reyes, 157 F.3d 949, 955 (2d Cir.1998) (internal citations and quotation marks omitted).
Defendants first argue that the evidence did not support the convictions for conspiracy to pay a kickback because their payment of $100,000 to a fund attorney was a gratuity rather than a bribe. The crimes of bribery and illegal gratuity differ as to their intent elements. “Bribery requires intent ‘to influence’ an official act or ‘to be influenced’ in an official act, while illegal gratuity requires only that the gratuity be given or accepted ‘for or because of an official act.” United States v. Sun-Diamond Growers, 526 U.S. 398, 404, 119 S.Ct. 1402, 143 L.Ed.2d 576 (1999) (quoting 18 U.S.C. § 201(b)(1) (bribery) and 18 U.S.C. § 201(c)(1) (illegal gratuity)).
However, the kickback statute that defendants conspired to violate, 18 U.S.C. § 1954, punishes a person who pays illegal gratuities as well as bribes, i.e., “any person who directly or indirectly gives or offers, or promises to give or offer, any fee, kickback, ... or thing of value” to a trustee of an employee welfare benefit plan “because of or with intent to ... influence [ ] ... any of [the trustee’s] actions.” Id. § 1954; cf. United States v. Glick, 142 F.3d 520, 524, 526 (2d Cir.1998) (noting that the giving of a gratuity rather than a bribe may impact the severity of the sentence imposed for violating 18 U.S.C. § 1954).
Defendants also, contend that the evidence was insufficient to support the two substantive wire fraud convictions because the government failed to prove the use of wires.
The first substantive wire fraud count involved a letter bearing the legend “via fax,” which was sent from a law firm in New Jersey to the pension fund’s offices in Queens, New York. Ileana Gomez, a secretary at the law firm, testified that she typed the letter, that it was her practice to type on a document the means by which the document was to be transmitted, and that if the sender had changed the means of transmission, she would have re-typed the letter to reflect the change.
On this evidence alone, the jury rationally could have concluded that a facsimile machine was used to transmit the letter to the pension fund. See United States v. LaBarbara, 129 F.3d 81, 84 (2d Cir.1997) (government may prove the use of wires through circumstantial evidence, such as customary business practices) (mail fraud); United States v. Muni, 668 F.2d 87, 89 (2d Cir.1981) (interpreting the wire fraud statute by reference to caselaw construing the mail fraud statute); United States v. Huber, 603 F.2d 387, 399 (2d Cir.1979). In addition, the government adduced a facsimile cover sheet found in the law firm’s files that is (i) in Gomez’s handwriting, (ii) addressed to the pension fund, and (iii) bears the same date as the letter. The record contained no evidence of an alternate means of delivery.
The second substantive wire fraud count concerned a transfer of $150,242 from a bank in Geneva, Switzerland, Compagnie de Gestion et de Banque Gonet, S.A. (“Banque Gonet”), to Republic National Bank in New York City. Defendants hypothesize that instead of sending this money by wire transfer, Banque Gonet might have hired a courier to physically transport an instrument from Switzerland to the United States. However, (i) Banque Gonet’s account statement reflecting the $150,242 withdrawal included the marking “TRSF,” which other Banquet Gonet docu*79ments make clear is a designation for a wire transfer; and (n) the Republic National Bank statement showed a $40 deduction from the amount withdrawn from Banquet Gonet, an adjustment that, according to testimony of a Federal Bureau of Investigation agent who had analyzed all of the bank records, represented a “wire transfer fee.”
We have reviewed defendants’ remaining arguments concerning sufficiency of the evidence and, after careful consideration, find them to be without merit.
2. Constructive Amendment of the Wire Fraud Conspiracy Count
Count Two of the superseding indictment accused the defendants of conspiring to defraud the pension fund of money through the use of wire communication in interstate and foreign commerce. As part of the scheme to defraud, the defendants allegedly misrepresented to the pension fund that its investment would remain in a bank account in the United States under the control of the fund’s attorneys, whereas in fact the money was transferred to a Swiss bank account over which the attorneys had no control.
Defendants argue that the government constructively amended this charge at trial by introducing evidence that, subsequent to the overseas transfer, defendants paid themselves commissions from the Swiss account without the fund’s permission. This evidence assertedly allowed the jury to convict defendants of embezzlement or conversion rather than fraud, in violation of the Grand Jury Clause of the Fifth Amendment. See Stirone v. United States, 361 U.S. 212, 215-16, 80 S.Ct. 270, 4 L.Ed.2d 252 (1960).
“To prevail on a constructive amendment claim, a defendant must demonstrate that either the proof at trial or the trial court’s jury instructions so altered an essential element of the charge that, upon review, it is uncertain whether the defendant was convicted of conduct that was the subject of the grand jury’s indictment.” United States v. Frank, 156 F.3d 332, 337 (2d Cir.1998) (per curiam). “Because proof at trial need not, indeed cannot, be a precise replica of the charges contained in the indictment,” we have “consistently permitted significant flexibility in proof, provided that the defendant was given notice of the core of criminality to be proven at trial.” Id. at 338 (quoting United States v. Heimann, 705 F.2d 662, 666 (2d Cir.1983)).
Judge Amon rejected the constructive amendment argument at trial, when defendant Dass invoked it in seeking to preclude evidence of the improper commissions. The district court ruled that the defendants’ looting of the account was “probably the most salient fact in the case,” and that it would be hard to imagine “anything more relevant” to a fraud case than the fact that the defendants “took money without permission.” We agree with the district court, and therefore reject defendants’ constructive amendment argument.
We have considered defendants’ remaining arguments and find them to be without merit. For the reasons set forth above, the judgment of the district court is hereby AFFIRMED.