All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
We have not read or heard about the poem you are asking about. Our righteous predecessors did not used to recite Islamic rhymes or poems when a person dies or at sacred nights. We have already issued Fatwa 86186 on the ruling of reciting poems on the Prophet's birthday, and issued Fataawa 81765 and 89739 clarifying that it is an innovation to celebrate the Prophet's birthday, so please refer to them.
Allaah Knows best.