Is it obligatory to donate the stolen money with the intention of its owners, given that its original source is no longer remembered, along with the prior intention of stealing and subsequent repentance?

The fundamental principle is the presumption of innocence. So, unless you are certain or highly confident that you took someone else's money unjustly, then you are not accountable. Otherwise, repentance and returning rights to their owners are obligatory. Therefore, you are required to give back what you are highly confident you took unjustly and strive to identify its owner. It is not permissible to give the money in charity as long as you know its owner and are able to return it to them. It is sufficient to deliver the money to them by any indirect means without disclosing the matter to them.