Muhammad Taqi bin Ali Reza compiled "Athar-i Muhammadi" in 1310/1893, dealing with the history of the Ismaili Imams. It relates one incredible story that Kiya Buzrug Ummid had made a will to his son, Muhammad bin Kiya that he must give up the power in favour of al- Mohtadi when he grew young. One day, when Muhammad bin Kiya asked about it to al-Mohtadi, the latter said, "This is the task of my son Hasan after our death." Muhammad bin Kiya feared to hear it, since al-Mohtadi had no male issue at that time. When al-Mohtadi was at death-bed, he summoned Muhammad bin Kiya, and said, "My wife is expecting a child. You take her to your house after me and do not make a little snag in her treatment. She will bear a son, whom you name "Hasan", because he will be like his forefather in beauty, virtue, knowledge, ethic, fame and grandeur. You must consider him as your own son, and deliver him the power." Thus, Muhammad bin Kiya acted upon these instructions.
Granted that the above story is historically genuine, then it implies that al-Kahir would have been born in 552/1157 immediately after the death of his father, al-Mohtadi. It determines the age of al-Kahir for five years when he died in 557/1162, which is absolutely false.
Secondly, the above story indicates the name of the son of al-Mohtadi as "Hasan" instead of al-Kahir, brushing off the historicity of al-Kahir. Granted for a while that the son of al-Mohtadi was Hasan, then it means that Hasan (or Hasan II) was hardly nine years old during his death in 561/1166, which is also unbelievable. In sum, the story of "Athar-i Muhammadi" referred to above is quite fictitious and contrary to the Ismaili traditions.
Al-Mohtadi was also taking care of the horses bred by his father in the fortress of Lamasar. He is also reported to have taken visits of surrounding castles in Rudhbar. He died in 552/1157 at the age of 52 years. He had vested the office of Imamate in his elder son, al-Kahir.