What is the ruling of Islamic law on claiming ownership, or a share, of lands that were designated as municipal grants under the names of other individuals, after their supporting documents had been submitted to obtain compensation for government land?

These plots are government grants, and each brother owns the land that was issued in his name. Your brother has no right to it, as long as the competent authorities have granted it to you, especially since the government owns the land that your brother laid claim to. If you decide to give your brother a portion of the land to preserve amity, that would be good.