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, sallallaahu ‘alayhi wa sallam, is His slave and messenger.
When the maternal grandmother (mother’s mother), paternal grandmother (father’s mother), maternal grandmother’s mother (mother of mother's mother), paternal grandmother’s mother (mother of father's mother), and the paternal grandfather’s mother (mother of father's father) are among the heirs, only the maternal grandmother (mother’s mother) and paternal grandmother (father’s mother) are entitled to inherit. They share one-sixth of the estate that should be equally divided among them. All other grandmothers are excluded from the inheritance. This is because the maternal grandmother’s mother is excluded by the presence of her daughter (i.e. the mother’s mother) and the paternal grandmother’s mother is excluded by the presence of her daughter as well (the father’s mother).
Ibn Qudaamah said, “If one of the grandmothers is the mother of the other, scholars unanimously agreed that the closer one (in lineage) causes the more distant (in lineage) grandmother to be excluded from the inheritance …” [Al-Mughni]
As for the mother of the father's father, although she is (sometimes) entitled to a share of the inheritance according to the view of the majority of scholars, she is excluded in this case due to two reasons:
First, she is excluded by the presence of the mother’s mother; because the close maternal grandmother obstructs the distant paternal grandmother from the inheritance. Ibn Qudaamah wrote about the presence of more than one grandmother with regards to inheritance, “If the closer grandmother is on the mother’s side and the distant one is on the father’s side, the close maternal grandmother obstructs the distant paternal grandmother according to most of scholars.” [Al-Mughni]
Second, she is also excluded by the presence of the father’s mother, even though they are both on the father’s side. This is because the father’s mother is the closer to the deceased (than the mother of the father's father). Al-Mawsoo‘ah Al-Fiqhiyyah (Fiqh Encyclopedia) reads, “Scholars unanimously agreed that the grandmother who is closer in lineage to the deceased osbtructs the distant one if they are both from the same side.”
Lastly, we would like to point out that scholars held different opinions regarding whether the mother of the father’s father is entitled to inherit or not. The majority of Muslim scholars maintained that she is among the eligible heirs. However, other scholars held that she is not entitled to inherit. Imaam Al-Nawawi wrote, “As for the mother of the father’s father and whether she is among the eligible heirs or not, some scholars held that she is not entitled to inherit. This opinion was adopted by the scholars of Hijaaz: Az-Zuhri, Rabee‘ah, and Maalik because she is a mother of the father's father (an eligible heir), and hence, she is not entitled to inheritance just like the mother of the mother's father. Thus, only two grandmothers are entitled to inherit.
The second view is that she is entitled to inherit. This opinion was adopted by ‘Ali, Ibn Mas‘ood, Ibn ‘Abbaas, and is one of the two opinions reported from Zayd ibn Thaabit . Moreover, Al-Hasan Al-Basri, Ibn Seereen, scholars of Kufah, Ath-Thawri, Abu Haneefah and his followers adopted that opinion, which is the preponderant opinion in this regard.” [Al-Majmoo'] The Hanbali scholars also maintained that she is entitled to inherit.
Allaah Knows best.