How can I return the money I took from my deceased father, knowing that he bequeathed all his cash to charitable works and ongoing Sadaqah, and does my monthly payment to charitable works for his soul absolve me of this debt and sin?

The way to absolve oneself of this sin is through sincere repentance and returning the stolen money to the father's heirs. Donating the stolen money as charity is not sufficient as long as there are heirs. As for the father's will to dedicate all his cash to charitable deeds, it is not enforceable beyond one-third of the estate unless approved by the adult heirs. However, if all the cash, including the stolen money, does not exceed one-third of the estate, then the will is valid, and donating this money to charitable causes is permissible, because a bequest is valid for something unknown, non-existent, or impossible to deliver.