She refused to accept her share of her son’s estate; does it go to the rest of the heirs?
Question

A man died and left behind a mother who is over one hundred years old, and is still of sound mind. When the estate was divided, she refused to take her share (on the grounds that she would not accept the wealth of one who was dead). Now she is living with her other son, and when he asked her to sign or give her fingerprint to confirm that she was waiving her share, she refused. Her son was asked to sign instead of her, on the grounds that he was a witness to her rejection of the inheritance. Please note that the second brother has some outstanding debts owed to him by the deceased brother.
Praise be to Allah.The heir has the right to give up his share of the estate and to give it to someone else, so long as he is of sound mind, because he has the right to dispose of his wealth in whatever way he wishes.
It should be understood that in order for the inheritance to become the property of the heir, it is not stipulated that the heir should consent to that; rather his share automatically becomes his, so it is his property. Thus this mother’s share of her son’s estate automatically became hers, and she cannot refuse it, but she can give this share to whomever she wishes, and in the case of a gift, there is no stipulation of writing it down or recording it; rather recording things is done for the purpose of documentation, protecting people’s rights and avoiding accusations of wrongdoing.
Based on that, the mother should be informed that her share of her son’s estate is such and such, and that this share has become her property whether she likes it or not, and that she may forfeit it or give it to whomever she wishes. If she gives it to her other son, and she is of sound mind, that is permissible, on condition that she does not have any other children. If she has other children, then she must treat all her children fairly, and it is not permissible for her to favour one of them over the others.  That should be witnessed by two witnesses, and the son does not have the right to sign or put his fingerprint on her behalf.
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: Ownership of the estate is transferred automatically to the heir and it becomes his property (whether he likes it or not). Allah, may He be exalted, says (interpretation of the meaning):
{And for you is half of what your wives leave} [an-Nisa’ 4:12]
{And for one’s parents, to each one of them is a sixth …} [an-Nisa’ 4:11].
Hence if one of the heirs says: I am well-off and I do not want my inheritance from So-and-so, we say to him: Your inheritance is proven whether you like it or not, and you have no choice in the matter, but if you want to give it up to one of the other heirs or to someone else, then that is up to you, after it has come into your possession." (Ash-Sharh al-Mumti‘  6/142).
And he (may Allah have mercy on him) said: Ownership is transferred to the heir automatically, and becomes the property of the heir automatically, even if the heir wants to forfeit it and says: I do not want my share of the inheritance. He cannot do that, because Allah has given him possession of it. Allah, may He be exalted, says:
{And for you is half of what your wives leave} [an-Nisa’ 4:12]
{Allah instructs you concerning your children: for the male, what is equal to the share of two females} [an-Nisa’ 4:11].  
So it is not possible for him to forfeit that of which Allah has given him possession. Ownership is transferred automatically by inheritance, and the heir cannot refuse it. So if someone dies and leaves behind two sons, and one of them says: I am well off and I do not want this inheritance, can he do that? He cannot do it. Rather we say: It has automatically become yours because Allah has given you possession of it." (Ash-Sharh al-Mumti‘ 10/232).
If we assume that the mother does not agree to give it to anyone, then her share remains her property and is to be inherited from her when she dies. Her refusal to accept this share is not regarded as forfeiting it or giving it away, unless she clearly states that she is giving it away or forfeiting it, because her refusal is not valid. The wealth has become her property on the basis of certainty, and cannot exit her ownership except on the basis of certainty. Hence the way to deal with this matter is to make her understand and inform her of the ruling on this issue.
And Allah knows best.