Is it permissible for a person eligible in inheritance to take his share and then offer it as a gift to another person who is also eligible in the same inheritance (for example his brother)?

Praise be to Allah, the Lord of the World; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

It is permissible to give one's share of inheritance to another inheritor as long as a donor is sensible, pubescent and of full age. Such an action is a kind of gift, donation or charity, and it becomes sure and positive if the receiver is needy. In addition, such an action will be a form of Sadaqa and honoring ties of relations among a household.
Allah knows best.