[The Ruling on One Who Picks Up a Banknote]

Answer – and Allah is the One who grants success: The madhhab, as mentioned in the marginal notes, is that it is not obligatory to announce coins (dirhams) unless legal proof (bayyinah) regarding them is possible – such as when they are in a purse. End of quote.
I say: He is obliged to return it to whoever comes seeking it if a presumption of his truthfulness arises. Such a presumption may arise in the case of someone who comes seeking a specific banknote in a particular place, and informs that it slipped from his hand at a particular time. That is because the public calling out for lost property, the fact that it is a specific banknote, that the seeking of it is in a particular place, and that the loss occurred at a specified time – all of these are indications, the sum of which points to a presumption of the owner’s truthfulness. All of this is so long as the one who is seeking it has not heard that someone picked something up in that place.
As for when that (presumption) does not arise, he should give the dirham or the banknote in charity to a believing poor person, or to a student of knowledge, or the like – or to himself if he is deserving of it. The Prophet, May Allah bless him and his family and grant them peace, gave ʿAlī (Peace be Upon Him) permission to eat the dīnār that he had picked up.

Source: Min Thimār al-ʿIlm wa al-Ḥikmah vol.2