Is it permissible for my friend who stole money to give it away as charity on behalf of its owner, fearing exposure, and will Allah forgive him for that?

Your friend is obligated to repent and return the stolen money to its owners, or seek their forgiveness for it. Donating it on their behalf will not suffice. He is not required to inform the owners of the theft; rather, it is sufficient to return it to them through a means that does not result in harm or embarrassment.