What is the ruling on praying in a mosque next to which a structure has been built symbolizing the place of death of its builder, knowing that the builder was not buried there, and does this structure affect the validity of the prayer?

It appears that the deceased was not buried in the mosque courtyard. Rather, there is an area enclosed with bricks for remembrance, and prayer in this place is sufficient and does not need to be repeated. However, revering a place that Allah has not hallowed is not legislated.

Allah has not legislated any place to be specifically sought for prayer except the mosque, nor for worship except the sacred sites (Mashaa'ir). Other than these places, it is not recommended to seek them out for prayer, supplication, or remembrance, as there is no evidence in the Sacred Law to indicate this. For the religion is based on following the Prophet, peace and blessings be upon him, and considering something that he did not legislate as an act of drawing closer (to Allah) is a contravention of his teachings.

The congregational prayer in the mosque is valid. Those in charge of the mosque are advised to level the ground, remove the bricks, and erase the symbol that refers to the deceased, as a means of preventing excuses (for future innovations). What benefits the deceased most is increasing supplication for him, seeking forgiveness for him, and giving charity on his behalf.