It is the ownership for the poor; as he (peace be upon him) said: "Give on behalf of every free person and slave," in Sunan al-Daraqutni 2: 150, and the giving is the ownership, so it cannot be fulfilled with permissible food, and with what is not ownership at all. The conversion to Islam of the recipient is not a condition for the permissibility of the giving, so it is permissible to give it to the people of the covenant, and it is permissible to give what is required in the Zakat al-Fitr for one person to a group of poor people, and to give what is required for a group to one poor person; because the obligation is Zakat, so it is permissible to collect it and distribute it: like the Zakat of wealth, and the imam does not send a collector for it; because the Prophet (peace be upon him) did not send one, and we have a good example in this. See: Bada'i al-Sana'i 2: 74-75.