The primary crime that you have described is called money laundering.
Note that money laundering includes: "structuring financial transactions in order to evade reporting requirements."
Unlike some other forms of money laundering, this does not require that the source of the funds be criminal, or that the actual transfer be criminal, so long as it is intended to avoid reporting requirements. Along the same lines is the even less obvious offense of smurfing.
So, this does not cease to be money laundering because: "A legally possesses the money and has a perfectly legal (and very private) reason to pay it to B."
The transfer would typically have had to be reported on a Form W-2 (wage and salary income), a Form 1099 (most transfers that are usually taxable income), a Form 709 (gift tax return), a Form 1098 (mortgage interest), or 1040 Schedule A (deductible payments), or on a cash transaction form if conducted in that manner. The fact that you are reporting it as income, and that there would have been some disclosure requirement if paid to person B, implies that there is some reporting requirement that is avoided.
There are also multiple tax related crimes that could be implicated, not all of which require that taxes due by the person charged by reduced. See, e.g., Conspiracy to Defraud the United States (18 U.S.C. § 371); Attempts To Interfere With Administration of Internal Revenue Laws (I.R.C. § 7212); Fraudulent Returns, Statements or Other Documents (I.R.C. § 7207); Identity Theft (18 U.S.C. § 1028(a)(7)), etc.
Conspiracy to Defraud the United States, for example, is defined as follows:
If two or more persons conspire either to commit any offense against
the United States, or to defraud the United States, or any agency
thereof in any manner or for any purpose, and one or more of such
persons do any act to effect the object of the conspiracy, each shall
be fined under this title or imprisoned not more than five years, or
If, however, the offense, the commission of which is the object of the
conspiracy, is a misdemeanor only, the punishment for such conspiracy
shall not exceed the maximum punishment provided for such misdemeanor.f
"Conspiracy to defraud the government is a very broad concept." Tax Crimes Handbook at 132.
Conspiracy to defraud the government is not limited to efforts to
obtain money or property, but includes conspiracies where the object
of the conspiracy is to obstruct, impair, interfere, impede or defeat
the legitimate functioning of the government through fraudulent or
dishonest means. Thus, conspiracy to defraud is not confined by
reference to common law definitions of fraud. It is a separate crime
to interfere with the lawful functions of the government without
regard to the monetary consequences. Thus, § 371 involves both efforts
to defraud the government of funds as well as interference with the
lawful function of the government.
The conspiracy to defraud prong
of § 371 includes conspiracies to impede, impair, obstruct or defeat
the lawful functions of the Treasury Department in the collection of
income taxes. United States v. Klein, 247 F.2d 908, 915 (2d Cir.
1957), cert. denied, 355 U.S. 924 (1958). Arguments have been
presented that § 371 was not intended to encompass conspiracies to
violate the internal revenue laws or conspiracies to defraud the
Service but these arguments have been rejected.
Although decided in 1957, Klein is the leading case regarding
conspiracies to impede and impair the Service and such conspiracies
are commonly referred to as "Klein conspiracies." In Klein the
defendants were acquitted of the tax evasion charges but were
convicted on the conspiracy count. The wording of the conspiracy count
read, in part, as follows: "... to defraud the United States by
impeding, impairing, obstructing and defeating the lawful functions of
the Department of the Treasury in the collection of the revenue; to
wit, income taxes." In part, it was alleged in Klein that as "part of
said conspiracy that the defendants would conceal and continue to
conceal the nature of their business activities and the source and
nature of their income." The defendants concealed the source and
nature of their income by altering and making false entries in their
books, filing false income tax returns, and providing false answers to
Thus, a money laundering plan may result in a conspiracy to obstruct
the Treasury. United States v. Sanzo, 673 F.2d 64, 69 (2d Cir.), cert.
denied, 459 U.S. 858 (1982). In Sanzo, one defendant argued that there
was no direct evidence that the other party to the plan would not
report the laundered money or claim deductions. The court felt there
was enough circumstantial evidence from which the jury could find that
the defendant knew his accomplice would not report large sums of
laundered money as income and that he would have to falsify business
records to hide the laundering activities. Sanzo, 673 F.2d at 69.
Note, it is not necessary to prove that the Service was actually
impeded in its efforts to assess and collect the revenue.
Tax Crimes Handbook at 132-136 (in the pertinent parts, with most citations omitted).
Caveat Regarding Legal Alternatives
It is also worth noting that there are legal ways for person A to transfer money to person B without making it apparent, for example, in his check book or on his tax return that the funds were transferred to person B (exactly how is beyond the scope of this answer).
Generally speaking, they are distinguishable because the IRS is fully and accurately informed of what is going on in a way that the IRS is not allowed to disclose publicly.
But, the crude method used here does not achieve that end.