Is it permissible to give Zakat al-Fitr on behalf of the deceased?

Zakat al-Fitr is obligatory upon a living Muslim who reaches the time of its obligation, which is the sunset of the last day of Ramadan. So, whoever dies before this time, it is not obligatory upon him. As for whoever reaches it and then dies before giving it out, it is to be taken from his wealth. If the deceased dies before the sunset of the night of Eid, then his Fitr [Zakat] is not obligatory. If charity is given on his behalf, it is a beneficial charity for him, but it is not Zakat al-Fitr.