Rav Avrohom ben HaRambam, the only son of the Rambam, was born to him by his second wife. He was born in Fostat, Egypt and is the mechaber of HaMaspik L’avdei Hashem as well as Shu"t is Birkas Avrohom https://hebrewbooks.org/43006He also composed a commentary to the Torah discussed here http://www.daat.ac.il/daat/kitveyet/sinay/nevo-4.htm
Rav Avrohom was born around 4946/1186 in Fostat (Ancient Cairo) in Egypt. The Rambam was fifty-one when his only son was born.
The Rambam said that although the custom was for Egyptian and Sefardic Jews, including the Maimon family to name after ancestors, he named his son Avrohom after the first believer, our forefather Avrohom Avinu.
He merited to study under his great father, and the Rambam writes in one of his many letters to his talmid Rav Yosef Bar Yehuda, to whom he dedicated the Moreh Nevuchim, that “my son Avrohom has been blessed and granted by Hashem chen – natural beauty – from the blessing of whom he was named after [Avrohom Avinu] and from Him in Whom Avrohom believed, may he continue to live a long life. He is humble and lowly and possessed of good character traits. He has a sharp, refined mind and is good-natured, and with G-d’s help he will be counted among the great names of famous Rabbonim without a doubt. I shall ask of Hashem to watch over him and complete His kindness.”
Rav Avrohom was privy to many of his father’s chiddushim on Tanach, as well as various philosophical ideas and explanations of his father’s thought.
At age seventy, the Rambam passed away, when his son Rav Avrohom was only nineteen years old, and at this young age the yoke of leadership of the Egyptian Jewish community fell on his shoulders.
He was given the title Noggid, a hereditary position that was passed down in an unbroken chain from father to son in the Maimonides family for five generations. Among the powers of the Noggid was the appointment of dayonim, and all the Egyptian communities were under his watchful eye as is testified by the many manuscripts that remain from the genizah signed “by permission of our master the Noggid Rav Avrohom.” Besides his public post, Rav Avrohom also took over his father’s position as chief physician to the Sultan’s royal court.
Rav Avrohom’s magnum opus was the Arabic language work named in Hebrew translation Sefer Hamaspik Le’ovdei Hashem, an encyclopedic work that covered all aspects of Yiddishkeit from Tefilla and Avoda to performance of mitzvos, mussar and character traits and their refinement.
He was also known as Rav Avrohom HeChassid and was a leader in the nascent Chassidic movement of Egypt and other Islamic lands, where they focused on kavona and davening and engaged in prostration in davening, which Rav Avrohom approved of.
Besides his great mussar work, Rav Avrohom also authored a commentary to the Tanach, of which we have fragments on Bereishis and Shemos. In his teshuvos we find several commentaries to the Neviim Rishonim, in which he focuses on peshat as opposed to deroshos and aggodos.
He also authored several works defending his father’s seforim: Birkas Avrohom, Maasei Nissim and Milchemos Hashem defending Moreh Nevuchim.
Like his father before him, Rav Avrohom ben HaRambam received letters asking for his psak and opinion on various matters of halocha and hashkofa (Jewish philosophy). He replied and sent letters back to all corners of the globe, including Egypt, Eretz Yisrael, Yemen and Europe. Scattered among the collections are over 130 extant responsa.
In his letters to other dayonim we find him urging again and again to love and respect and seek truth over victory. He himself testifies that this is his way emulating his great father and master. “Even if the smallest student in stature were to criticize me and prove me wrong using truth and he would be truly correct, we would agree with him and admit our mistake, as Chazal say ‘always admit the truth,’ and this is why the dayonim are known as anshei emes – men of truth and sincerity.”
He was niftar in Fostat.
