Should zakat ul-fitr be paid on behalf of a dead person in the first of Ramadan after his death?

No. When a person dies, he no longer has any devotional duties to perform. Zakat ul-fitr is obligatory for anyone who is alive at the time of Ramadan but not for one who dies before it. Consequently, it should not be paid either from his estate or on his behalf by any of his relatives.

And God Almighty knows best.