All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah and that Muhammad is His slave and Messenger.
As for the inheritance of the deceased father, if the eldest son died after his father, as it appears from the question, then the eldest son has a share in the inheritance of his father. If the son died before taking his share, then his share moves to his heirs, including his wife, who gets a quarter of his share as long as he has no children, as you mentioned in the question.
As for the inheritance of the mother who is still alive, then the wife of her son does not inherit from her if she dies. The wife of the son does not inherit from the mother of her husband, and she has no share in her mother-in-law’s inheritance.
It seems that with the information that you mentioned in the beginning of the question - that the deceased left one son and four daughters - you mean the mother who is still alive, and it seems that you are asking how her inheritance should be divided if she dies and leaves behind these heirs.
If this is what you mean, then the mother should not be preoccupied with how her inheritance should be divided after her death, as there might be other heirs than those mentioned in the question at the time of her death, and perhaps one of them might die before her; in which case the division of inheritance will be different.
Therefore, one should not guess how to divide the inheritance of a living person, and the Salaf (righteous predecessors) used to dislike being asked questions about what had not yet taken place, and if they were asked about such thing, then they would respond by saying, “Leave it until it happens.”
Also, according to the sharee'ah, she is not obliged to write a will about the division of her inheritance.
In any case, we would say that if she dies and leaves behind one son and four daughters, and she does not leave any other heir, then her inheritance should be divided by ta’seeb (by virtue of having a paternal relation with the deceased and not having an allotted share, so they get what is left after the allotted shares have been distributed); the male twice the share of the female, as Allaah says (what means): {Allaah instructs you concerning your children [i.e. their portions of inheritance]: for the male, what is equal to the share of two females.}[Quran 4:11]
Therefore, the inheritance should be divided into six shares, the son gets two shares, and each daughter gets one share.
On the other hand, the mother distributing what she owns among her male and female children while she is alive is not considered a division of the inheritance; rather, this is considered a gift. This is because the division of the inheritance can only take place after she dies, and what she gives in her life is called a gift or a donation.
If she wants to divide her property between her son and her daughters while she is still alive, then she is permitted to do so, but she is obliged to be just between her children, as An-Nu’maan ibn Basheer narrated that the Prophet said, “Fear Allaah and be just when gifting your children.” [Al-Bukhari and Muslim]
Justice is achieved by her giving the same gift to the male and the female, or by giving the male twice the share of the female; according to the two opinions of the scholars. For more benefit, please refer to fatwa 314443.
Allaah knows best.