How can one atone for the sin of taking money and jewelry from one's wife's aunt without her knowledge and lying to her, if she refuses to forgive before her death?

Sincere repentance to Allah Almighty is obligatory, characterized by regret and a firm resolve not to return to the sin, along with the return of the money taken from the deceased without her consent to her heirs, based on the Prophet's (peace and blessings be upon him) saying: "The hand is responsible for what it took until it returns it." This requires an accurate calculation of these funds, or at least a strong presumption and taking precautions.