Muhammad or Mehmud Shah, generally called Muhammad bin Islam Shah is believed to have been born in Daylam. He was almost ten years old when his father arrived in Kahek in 798/1396. If this is a genuine tradition, it implies that he was born possibly in 788/1386, and was about 17 years old while assuming the Imamate. He mostly resided in Shahr-i Babak in Kirman.
The Iranian Ismailis began to revert to their former settlements in different villages. Most of them engaged in agriculture in Kohistan, Qain, Birjand, Nishapur, Khorasan, Sirjan, Jabal-i Bariz, Mahallat and Yazd.
Muhammad bin Islam Shah seems to have started communications from his headquarters to different Ismaili communities, and also accepted the gifts of the pilgrims. It is said that the Indian Ismaili pilgrims were invested the title of "darwish" (daras).
Taymur designated his grandson Pir Muhammad as his heir, who was about 22 years old in 807/1405. But, his cousin Khalil Sultan occupied Samarkand and was proclaimed as sultan. He was overthrown in 811/1409. Meanwhile, Shah Rukh (1409-1447), the fourth son of Taymur, the then governor of Herat, ascended as the next Taymurid ruler of Iran and Central Asia. He died in 851/1447 and was succeeded by his son Olugh Beg (1447-1449), who was in turn followed by Abu Sa'id (1451-1469).
One seminal point should not omitted here in discussion that the office of the hujjat or pir in India from Pir Shams (d. 757/1356) to Pir Hasan Kabiruddin (d. 853/1449) was almost hereditary, and then the office seemed to be revered like the hereditary office of the Imams, and therefore, an effect was necessary to enforce in the line of the pirs before the time it might become an ingrained belief. Thus, after the death of Pir Hasan Kabiruddin, Imam Muhammad bin Islam Shah designated his brother Pir Tajuddin, as a next hujjat or pir for Hind and Sind instead of any son, and one can hardly deny the logic springs from such designation.