Is it permissible for a mother to pay the expiation for breaking her fast (kaffarat as-siyam) to her poor son who has a meager income?

If the son is in need and independent of his parents, it is permissible to give him charity (sadaqah) and expiation (kaffarah). However, if he lives with them and they provide for him, it is not permissible to give him charity or food.