See, technically what you are doing is this:
Person A buys BTC for $10,000 and gifts is to person B.
Person B's cost basis is $10,000; if they sell it for $11,000, they owe whatever tax they owe in their home country.
Person B gifts $11,000 (or $10,500 if you like) to person A. Since gifts are not taxable to the recipient, person A owes no income tax.
In other words, a classic tax-avoidance scheme that is highly illegal and has sent more than one person to prison (when the amounts are larger, of course).
And since bank and wire transfers of more than $10,000 are automatically reported to the IRS, there is no hiding this. (And splitting it into multiple transactions of less than $10,000 to avoid reporting is an entirely separate crime called "Structuring.")
Potentially you could enter into some kind of agency agreement where you remain the owner and you pay the agent a commission, but that would require attorneys knowledgeable in the law in both countries.
