Is it permissible for a brother to give out Zakat al-Fitr from the food his brother gave him as Zakat al-Fitr, when he is in need?

If the brother is poor, it is permissible to give him Zakat al-Fitr. By receiving it, he takes ownership of it, and it becomes permissible for him to pay it on behalf of himself and those whose maintenance is obligatory upon him. He is not required to pay his Zakat al-Fitr from his own private money.