Is it obligatory to return money found among discards belonging to the grandmother who permanently resides with the questioner, or is it permissible to use it for personal needs? And what is the jurisprudential ruling on this matter?

The found item (Luqata) must be preserved and announced for a full year in places frequented by people. After that, the one who found it may own it or donate it as charity, while guaranteeing its value to its owner if he is found and accepts the guarantee, or if he does not accept the charity. If a sum of money is found among the grandmother's belongings, she must be asked about it. If it belongs to her, it must be returned to her, and it is not permissible to use it without her permission. Otherwise, the rulings of Luqata apply to it.