What is the ruling on someone who stole money from his mother and sister without their knowledge, then repented and wishes to return the money to its owners without their knowledge? And is it permissible to give charity with the intention of delivering the reward to the deceased mother?

Congratulations to you on the blessing of repentance. Part of the completeness of your repentance is to return the money you took to its rightful owners. You must estimate the amount of money you took, and be careful in your estimation, so as to return the amount that you predominantly believe will absolve your conscience. Return your mother's share to her heirs according to their legal inheritance proportions, and your sister's share to her. You are not required to inform your sister or your mother's heirs of what happened; it is sufficient to return the money through any indirect means. Giving charity on behalf of your mother does not absolve your conscience as long as it is possible for you to deliver the money to its rightful owners.