What is the ruling on profits resulting from trading U.S. dollars that were acquired through a previous impermissible transaction, and is it permissible to benefit from them after ceasing such dealings?

Currency exchange is the selling of currencies for one another. It requires immediate, hand-to-hand possession (qabdh) at the contracting session without delay. If the two parties separate before taking possession, the exchange becomes void.

What you did, by delaying possession, is void. Each of you should take back their money. If the exchange has already been completed, it becomes a debt upon the one who took possession, who must return its equivalent.

As for the profits resulting from void exchange transactions, they must be returned to their owners. However, if the funds from void exchange transactions were used in permissible commercial dealings and generated profits, those profits are permissible because banknotes are not designated by specific identification. You are obligated to return what you owe from those void exchange transactions.