Is it permissible for the owner of a phone repair shop to refuse to hand over a customer's phone after two or three months have passed since the agreed-upon delivery date, due to the customer's failure to pay on time?

It is permissible for you to stipulate to phone owners that they must collect their devices within a specified period. After this period expires, you have the right to dispose of the phones by selling them, taking your labor fee, and retaining the remainder for their owners. If they return, you pay them what remains of their phones' value. If they do not return, you can give the remainder in charity on their behalf. It is preferable to agree upon this when the phones are handed over.

Merely placing a sign in the shop is not sufficient; this condition must be explicitly stated to each customer, or included in the invoice with a notice to the customer.

In a fatwa (definition) from the Permanent Committee, if owners of goods (watches in this case) leave their merchandise for a long time and you incur damage from that, you are permitted to sell them and give their price in charity on behalf of their owners, while taking your right to the repair fee. If one of the owners of the goods returns, he either accepts the situation, or you compensate him with the value, and the charity is considered your remuneration.