What is the ruling regarding the action of the son who, along with his brother, bought land and built upon it, then it was registered in the name of the father who has passed away, knowing that the heirs are aware that the land and the building were purchased with the money of the two sons, and what is the legitimate solution for this issue?

If the land was registered in the father's name as an honor and tribute to him, and not as an act of ownership transfer through gift or sale, then, Islamically, the house is not considered part of the father's estate, and the heirs have no right to it. This is because, in contracts, what matters are the intentions and meanings, and a nominal registration does not transfer ownership.