Some of the heirs gave up their share of the estate to the children and wife of their brother; how should it be divided among them?
Question

                A man died who had a mother, wife and children, and according to sharee‘ah the estate should be divided among them.

But before the estate was divided, the man’s mother died, and she had eight children, five male and three female. Hence they are entitled to inherit from their mother, but three of the sons said that they would give up their share of inheritance to the children and wife of the man who died.

My question is: should this portion that they have given up be divided according to sharee‘ah, because it is part of the inheritance, or should it be divided equally among the wife and children of the deceased?
Praise be to Allah.
      With regard to the man who died and left behind a mother, wife, and 
      children, his estate is to be divided as follows: 

    Firstly: the mother is entitled to one sixth, because there are descendants 
    who inherit from him. That is because Allah, may He be exalted, says 
    (interpretation of the meaning):

    “For parents, 
    a sixth share of inheritance to each if the deceased left children; if no 
    children, and the parents are the (only) heirs, the mother has a third; if 
    the deceased left brothers or (sisters), the mother has a sixth”

    [an-Nisa’ 4:11]. 

    Secondly: the wife is entitled to one eighth, because there are descendants 
    who inherit. That is because Allah, may He be exalted, says (interpretation 
    of the meaning):
“In 
    that which your wives leave, your share is a half if they have no child; but 
    if they leave a child, you get a fourth of that which they leave after 
    payment of legacies that they may have bequeathed or debts. In that which 
    you leave, their (your wives) share is a fourth if you leave no child; but 
    if you leave a child, they get an eighth of that which you leave after 
    payment of legacies that you may have bequeathed or debts”

    [an-Nisa’ 4:12]. 

    Thirdly: with regard to the children, they are entitled to the remainder of 
    the estate, after the mother and wife have taken their shares, and they 
    should divide it among themselves with each male getting the share of two 
    females. 

    Once it is established that the mother gets one sixth, she is entitled to it 
    and it becomes her property as soon as her son has died. Then if she dies 
    before the estate is divided, her share from her son who died is to be taken 
    from his estate as if she were still alive, then it is inherited by her 
    heirs, along with the rest of her wealth. However it should be noted that 
    inheritance becomes irrevocably part of a person’s property, but if he wants 
    to give it up after that to some of his heirs, there is nothing wrong with 
    that. Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: Taking 
    possession by means of inheritance is something irrevocable, and it becomes 
    the heir’s property whether he likes it or not. Allah, may He be exalted, 
    says (interpretation of the meaning):

    “In that which your wives leave, your share is a half”

    [an-Nisa’ 4:12]

    “For parents, a sixth share of inheritance to each”

    [an-Nisa’ 4:11].

    Hence if one of the heirs says: I am rich and I do not want my inheritance 
    from So and so, we say to him: Your inheritance is proven whether you want 
    it or not, and it is not possible for you to avoid it. But if you want to 
    give it up to one of the other heirs or to someone else, that is up to you 
    after it has come into your possession.

    End quote from ash-Sharh al-Mumti‘ (6/142) 

    Based on that, if the share of these three sons from their mother’s estate 
    has been decided, whether that is from all of her estate or from this 
    portion that she inherited from her son who died, then after knowing what it 
    is they may give it up to their brother’s children or to anyone else, 
    however they wish. 

    Moreover, what they have given up comes under the rulings on gifts, with 
    regard to the manner in which it is to be divided. If they say it should be 
    divided equally, then it should be divided equally among them, but if they 
    say that it should be divided among them according to the shares of 
    inheritance that each of them would receive according to sharee‘ah, then it 
    should be divided among them accordingly. If they stipulated some other way 
    of dividing it, in which some individuals are given more than others, then 
    they also have the right to do that. What they have given up is not an 
    inheritance or a gift from a parent in which it is obligatory to be just and 
    fair in sharing it out. 

    And Allah knows best.