Is it permissible to return stolen money by making the victim believe that the amount was sent by an unknown person? And will Allah forgive the sin with repentance and a commitment not to steal again? And what should a thief do if he cannot accurately determine the exact amount stolen?

It is obligatory to return rights to their owners, and it is not necessary to inform them about the theft. The method mentioned for delivering the money is good if the owner understands that it is his money. If it is difficult to inform the person from whom the theft occurred, the money can be delivered to him through indirect means, or by giving it as charity with the intention that it is for its owner if his whereabouts are unknown. If the amount of the right is unknown, an effort should be made to estimate it in a way that clears one's conscience.