Is it permissible to donate the value of a piece of gold that a father gave to his daughter, knowing that it belongs to her sister, and to dedicate the reward to the sister, without revealing the father's secret? And does this absolve the father of sin?

If the gold piece belongs to the sister, then one's responsibility is not absolved except by returning it to her or by seeking her forgiveness. If the father acquired it from the sister (through purchase or gift), then it becomes part of the heirs' property, and it is to be divided among them according to their prescribed shares. It is not permissible for whoever took it to keep it exclusively unless with the consent of the heirs, because a gift from the deceased during death sickness or a will made to an heir is not enforceable except with the permission of the rest of the heirs. General forgiveness is not sufficient to absolve oneself from financial rights; rather, the owner of the right must be informed of the exact amount of money taken from them. Returning the right does not necessitate exposing the father; rather, the right can be delivered without that.