Is it permissible for a divorced mother to pay Zakat al-Fitr on behalf of her children to her poor ex-husband?

Zakat al-Fitr is obligatory upon anyone who possesses more than their and their dependents' sustenance for the day and night of Eid. A man is responsible for paying Zakat al-Fitr for his minor children who do not own any wealth. However, if they do possess wealth, the Zakat is to be paid from their own wealth. If the mother provides for her minor children, she is obligated to pay their Zakat if they do not own any wealth. A divorced woman may give her Zakat and her children's Zakat to her poor ex-husband, even if it is likely that he will spend the money on the children, because the money is hers and not the children's. The return of the money to the giver in another form does not invalidate the Zakat, just as a wife may give Zakat to her husband, or as if someone paid Zakat to a debtor and then received it back as part of a debt repayment. This is affirmed by the hadith of Umm Atiyyah al-Ansariyyah, may Allah be pleased with her, that the Prophet, peace and blessings be upon him, said concerning charity that reached its rightful recipient: "Indeed, it has reached its proper place."