Is it obligatory to return ill-gotten gains to their owner who has repented, or to give them away in charity on their behalf?

Theft is a grave sin (kabirah) whose punishment is the cutting off of the hand, and it indicates a deficiency in faith. The thief must repent sincerely (tawbah nasuh), increase in righteous deeds, and return the stolen money to its owner, or seek forgiveness from him, even if the owner of the money does not pray or give charity. Judging a person's money as unlawful requires knowledge of all their sources of income, which is difficult.