I saw a sign hanging in my apartment building that read: “I lost an expensive coat with my name written on the inside label. $50 reward for its return.”
When I read the sign, I immediately thought of a coat that has been hanging on the coat rack in my yeshiva for the past few weeks. I went to check it, and indeed, it seemed that it was the lost coat.
When I returned the coat to its grateful owner, he wanted to pay me the fifty dollars that he had promised.
Q: Am I permitted to accept payment for performing this mitzvah?
A: Shulchan Aruch (C.M. 265:1) writes that one who sees a lost object is obligated to return it to the owner without reimbursement for his efforts. On the other hand, one is not obligated to suffer a financial loss to fulfill this mitzvah, even if it is lost profit rather than a loss of capital. According to some authorities, it is even prohibited to accept payment for returning a lost object, similar to the prohibition on accepting payment for teaching Torah (Rosh Bava Metzia 2:24, see Bechoros 29a). Therefore, the finder cannot accept any reward for fulfilling the mitzvah, whether he wants to charge money or if the owner of the object wants to pay him for the return (Machaneh Ephraim: Sechirus 15).
Other authorities contend that the prohibition for not accepting a reward for fulfilling a mitzvah is limited to Torah study (Rashi to Gemara Bechoros). Nevertheless, since the finder is obligated to fulfill the mitzvah, he may not only agree to fulfill this mitzvah for payment, and as such, he may not demand payment for that mitzvah. Furthermore, if the finder refuses to return the lost object without reimbursement, he would be a thief (Even HaAzel: Gezeilah 12:3). On the other hand, if the owner voluntarily wants to pay the finder for his efforts, the finder may accept those monies.
All of the above applies if the finder was never approached by the owner to find the lost object, directly or otherwise, e.g. a sign that promises a reward for the finder.
It would seem that all opinions would agree in your case that you may accept the money. In this case, since the owner indicated that he was willing to reward the finder, what he is essentially doing is hiring the potential finder to find his lost object. Although it is a mitzvah for one who notices a lost object to return the item, there is no obligation to search for someone’s lost things.
As such, since the payment is for the one who is willing to search and find the lost object, it is certainly permitted to accept the $50 reward, like any remuneration for work (see also Teshuvos V’hanhagos 3:463).