Is it permissible to donate the value of stolen goods instead of returning them to their owners, after the shop owner has forgiven me?

If the owner of the right forgives, then the debt is cleared, and there is no obligation to give charity, because the obligation to give charity for the right only applies when one is unable to reach its owner. If you wish to draw closer to Allah by giving charity with this money, then charity is a good and permissible act.