What is the ruling on the theft committed by the mother in this case, and what should the son do with the stolen banknote he possesses, and is it permissible to give it away as charity?

You are not to accuse your mother or search her belongings. The money must be returned to its owner through a clever stratagem that does not expose the secret, and it is obligatory to conceal your mother's fault and not inform anyone about the matter.