Question: Who is Isma'Il Ibn Ja'Far's paternal grandmother?

Knowledge 1: Isma'il ibn Ja'far
Ismāʿīl ibn Jaʿfar al-Mubārak (c. born: 719 AD, Medina - died circa 762 AD, Medina)was the eldest son of Imam Ja'far al-Sadiq.He is also known as Isma'il Al-Ãraj ibn Ja'far(اسماعيل الاعرج ابن جعفر الصادق).Following Ja'far's death, the Shia community split between those who believed the Imamate was passed to Musa ibn Ja'far, who would become the Twelver Shia, and those who believed that the Imamate passed to Isma'il ibn Ja'far, who would become the Isma'ili branch named after Isma'il. [SEP] Knowledge 2: Ja'far al-Sadiq
Jaʿfar ibn Muḥammad aṣ-Ṣādiq (700 or 702–765 CE), commonly known as Ja'far al-Ṣādiq or simply as-Sadiq (The Truthful), was an 8th-century Muslim scholar and scientist.He is considered as an Imam and founder of the Ja'fari school of jurisprudence by Twelver and Isma'ili Shi’as, and a major figure in the Hanafi and Maliki schools of Sunni jurisprudence.He was a descendant of the Caliph Ali and Fatimah bint Muhammad on the side of his father, Muhammad al-Baqir, and of Muhammad ibn Abu Bakr on the maternal side of his family, Umm Farwah bint al-Qasim.Muhammad ibn Abi Bakr was raised by Ali, but was not his son.Ali used to say: "Muhammad Ibn Abu Bakr is my son but from Abu Bakr's lineage".Al-Sadiq is the 6th Imam for Twelvers, is recognized by the majority of the Shi’a as an Imam, and is revered in Sunni Islam as a transmitter of hadiths, therefore a prominent jurist, and a mystic to Sufis.Despite his wide-ranging attributions in a number religious disciplines, no works penned by Ja'far himself remain extant.Al-Sadiq was born in either 700 or 702 CE.He inherited the position of imam from his father in his mid-thirties.As a Shi’a Imam, al-Sadiq stayed out of the political conflicts that embroiled the region, evading the many requests for support that he received from rebels.He was the victim of some harassment by the Abbasid caliphs, and was eventually, according to Shi’a Muslims, poisoned at the orders of the Caliph Al-Mansur.In addition to his connection with Sunni schools of Sunni jurisprudence, he was a significant figure in the formulation of Shia doctrine.The traditions recorded from al-Sadiq are said to be more numerous than all hadiths recorded from all other Shia imams combined.As the founder of Ja'fari jurisprudence, al-Sadiq also elaborated the doctrine of "Nass" (divinely inspired designation of each imam by the previous imam), and "Ismah" (the infallibility of the imams), as well as that of Taqiyyah.The question of succession after al-Sadiq's death was the cause of division among Shi’a who considered his eldest son, Isma'il (who had reportedly died before his father) to be the next Imam, and those who believed his third son Musa al-Kadhim was the imam.The first group became known as the Ismailis and the second, larger, group was named Ja'fari or the Twelvers.
Knowledge 1: Ja'far al-Sadiq
Jaʿfar ibn Muḥammad aṣ-Ṣādiq (700 or 702–765 CE), commonly known as Ja'far al-Ṣādiq or simply as-Sadiq (The Truthful), was an 8th-century Muslim scholar and scientist.He is considered as an Imam and founder of the Ja'fari school of jurisprudence by Twelver and Isma'ili Shi’as, and a major figure in the Hanafi and Maliki schools of Sunni jurisprudence.He was a descendant of the Caliph Ali and Fatimah bint Muhammad on the side of his father, Muhammad al-Baqir, and of Muhammad ibn Abu Bakr on the maternal side of his family, Umm Farwah bint al-Qasim.Muhammad ibn Abi Bakr was raised by Ali, but was not his son.Ali used to say: "Muhammad Ibn Abu Bakr is my son but from Abu Bakr's lineage".Al-Sadiq is the 6th Imam for Twelvers, is recognized by the majority of the Shi’a as an Imam, and is revered in Sunni Islam as a transmitter of hadiths, therefore a prominent jurist, and a mystic to Sufis.Despite his wide-ranging attributions in a number religious disciplines, no works penned by Ja'far himself remain extant.Al-Sadiq was born in either 700 or 702 CE.He inherited the position of imam from his father in his mid-thirties.As a Shi’a Imam, al-Sadiq stayed out of the political conflicts that embroiled the region, evading the many requests for support that he received from rebels.He was the victim of some harassment by the Abbasid caliphs, and was eventually, according to Shi’a Muslims, poisoned at the orders of the Caliph Al-Mansur.In addition to his connection with Sunni schools of Sunni jurisprudence, he was a significant figure in the formulation of Shia doctrine.The traditions recorded from al-Sadiq are said to be more numerous than all hadiths recorded from all other Shia imams combined.As the founder of Ja'fari jurisprudence, al-Sadiq also elaborated the doctrine of "Nass" (divinely inspired designation of each imam by the previous imam), and "Ismah" (the infallibility of the imams), as well as that of Taqiyyah.The question of succession after al-Sadiq's death was the cause of division among Shi’a who considered his eldest son, Isma'il (who had reportedly died before his father) to be the next Imam, and those who believed his third son Musa al-Kadhim was the imam.The first group became known as the Ismailis and the second, larger, group was named Ja'fari or the Twelvers. [SEP] Knowledge 2: Ibn 'Ulayya
Abu Bishr Isma'il ibn Ibrahim ibn Muqsim, commonly known as Ibn' Ulayya, was a hadith scholar, faqih and a mufti from Basra.
Knowledge 1: Isma'il ibn Ja'far
Ismāʿīl ibn Jaʿfar al-Mubārak (c. born: 719 AD, Medina - died circa 762 AD, Medina)was the eldest son of Imam Ja'far al-Sadiq.He is also known as Isma'il Al-Ãraj ibn Ja'far(اسماعيل الاعرج ابن جعفر الصادق).Following Ja'far's death, the Shia community split between those who believed the Imamate was passed to Musa ibn Ja'far, who would become the Twelver Shia, and those who believed that the Imamate passed to Isma'il ibn Ja'far, who would become the Isma'ili branch named after Isma'il. [SEP] Knowledge 2: Ibn 'Ulayya
Abu Bishr Isma'il ibn Ibrahim ibn Muqsim, commonly known as Ibn' Ulayya, was a hadith scholar, faqih and a mufti from Basra.

Answer: Farwah bint al-Qasim