Is it permissible to consider the Zakat on money and the charity with which the brother paid off his debt sufficient and fulfilling after Zakat al-Fitr has been paid by another person?

The basic principle for Zakat (definition) al-Fitr is that it should be given as food, and this is the view of the majority of scholars. It is permissible to appoint an agent (wakil) to distribute the Zakat. If the giver (muzakki) intends the Zakat at the time of setting aside the money and handing it over to the agent, and the agent then distributes it, that is sufficient for the giver. It is also permissible for the giver to instruct his agent to distribute the Zakat from the agent's private funds, and then the giver repays him. If the giver sets aside a sum of money with the intention of it being Zakat, it does not become designated as Zakat until the rightful recipient takes possession of it.