Is it permissible to buy something to replace what was lost by a relative to compensate him without informing him, since the borrower has forgotten about the matter?

The sister who asked the question made two mistakes: first, by not taking the initiative to return the borrowed item and being complacent until it was lost; and second, by neglecting her duty and handing it over to others without informing them to return it to its owner.

She must repent and ask those with whom she left the borrowed item. If she finds it, she should return it. If it was damaged, she is responsible for replacing it with a similar item if a likeness exists, or with its value if no likeness exists. She is not obligated to inform its owner that it is a likeness, not the original item itself.