What is the ruling on disposing of delayed Zakat al-Fitr: should it be directed towards the expenses of the mosque that covers its own costs, or towards a Sharia school where his son is acquiring knowledge? And does this affect the reward of those who paid the Zakat?

Zakat al-Fitr must be given before the Eid prayer. Delaying it without a valid excuse is a sin, and it then becomes an ordinary charity (sadaqah) and not an accepted zakat.

Whoever delays it has sinned and must pay it immediately as a make-up (qada'), for it does not lapse. It must be given to those who are eligible, such as the poor and the needy. It is not permissible to use it for mosque expenses or to give it to a madrasah (religious school) unless there are eligible recipients of zakat within it.

If there are no poor people in the giver's country, it is permissible to transfer the zakat to another country.