What is the method for returning stolen goods to their owner—whether directly or indirectly—and is it permissible to donate stolen money to the designated charity boxes in the mosque for those whose owners are unknown or for whom the amount stolen is unknown?

What was taken from the owner must be returned, either in kind or by value on the day of the theft if returning it in kind is not possible. Charity does not suffice if the owner can be reached, and direct return is not mandatory. As for those whose stolen amount you do not know, you must estimate what you believe, most likely, will clear your conscience. If you despair of reaching them, then spend it on charitable causes, such as charity boxes.