Is the distribution of inheritance mentioned in the question—in which some properties were relinquished—just and lawful, or does it represent an injustice to one of the parties?

What is distributed after the father's death with the consent of both parties, or with one party relinquishing their share to the other, is permissible. This is because a mature and رشيد (of sound judgment) individual has the right to dispose of their legal share. As for what the father did during his lifetime by way of a gift, if he did not treat his children fairly in it, then he has erred. He must be fair in giving gifts to his children. There are two opinions on how to be fair: either he gives the male the equivalent of the share of two females, or he gives the male the same share as the female. If the father bequeathed something from his estate to one of his heirs, this will is not binding and will not be executed unless the rest of the heirs approve it.