Can a brother give his brother a plot of land in exchange for the recipient waiving a sum of money he had previously given him, and for the difference in the price of the land that has increased?

If what transpired between you and your brother four years ago was a sales contract, then the land is yours. It is not a condition for registering the sale that it be in the seller's name with the official departments. As for the right of pre-emption (shufa'a), it is established for a partner in real estate before its division. However, after division, pre-emption is not obligatory for a neighbor according to the majority of scholars, based on Jabir's statement: "If the boundaries are set and the paths are allocated, then there is no pre-emption." Therefore, the neighbor does not have the right of pre-emption over land whose boundaries are distinct from his own. The sale should be officially documented to secure rights.