Is the questioner absolved of responsibility by returning the money to its owner without his knowledge, leaving it in front of his apartment door after he refused to receive it?

The questioner's statement: "He does not know who sent it or why" is incorrect, because he knows the reason: that the money was taken from him and is intended to be returned, and only the name remains unknown. The sender of the money (the questioner) is absolved as long as the owner of the money knows that this is his money, is able to take it, and the questioner has enabled him to do so. The fulfillment of rights occurs simply by enabling the right-holder to access what is due to him. If he refuses despite being able to take it, then the one who owes the right is absolved.