Praise be to Allah.
If the owner of the shop has stated that the customer must come and take the jewellery that he wants repaired within a period of no more than three months, then he does not come during that time period, then he may take his fee and give the rest of the gold in charity or sell it and give its price in charity; he should not take possession of it for himself.
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) was asked: In a Laundromat there are some clothes that have been there for more than two months and their owners are not known, even though one of the conditions on the receipt is that the Laundromat is not responsible for the clothes that are left by their owners for more than two months. Can the owner of the Laundromat take them, either to use them or sell them or give them in charity? If he takes them, then the owner asks for them after he has disposed of them, should he give the price of them or not?
If it is stipulated to the owner of the clothes that if he is two months late, he has no rights to the clothes he left, then he is the one who is late, and when the two months have passed, the owner of the Laundromat may either give them in charity if there is someone who will accept them and wear them, or he may sell them and give their price in charity. But I think that he should wait, after the two months, for 10 or 15 days, because the owner may have wanted to come, but his car broke down or he fell sick. So it is better to wait.
End quote from Liqa’ al-Baab al-Maftooh, 215/11
He also said: If there is a time limit agreed between them, then when that time ends, he may give them in charity or sell them and give their price in charity.
But if there was no set time agreed between them, it is not permissible to sell them after one or two months; rather he should not sell them and he should not dispose of them unless he has given up on the owner coming. If he has given up on him, then he is free (to dispose of them), because he cannot let his place become filled up with these clothes or these furnishings endlessly.
Liqa’ al-Baab al-Maftooh, 215/19
It should be noted that in the case of gold that is to be exchanged, it is not permissible to leave it in the shop, rather the exchange must be done in the same sitting, hand to hand, like for like; delaying it or giving more is riba.
Please see the answer to question number 74994.
And Allah knows best.