Ibn Abdul Bir in the book of AlIsti’aab v.1 p.425 Considered to be among the first books that were authored about the Sahaba: “Muhammad ibn Jaafer son of Abi Taleb, he is the one that married Um Kalthoom son of Ali Ibn Abi Taleb after the death of Umar Ibn Khattab”
AlBeri in AlJawhara v.1 p.205 speaking about Muhammad son of Jaafer(AlTayar)says “..as for Muhammad he is a look alike of Abi Talib and he is the one that married Um Kalthoom daughter of Ali.”
Asad AlGaba by Ibn AlAtheer v.2 p.481 “Muhammad son of Jaafer son of Abi Taleb:….”as for Muhammad he is a look-alike of our uncle Abi Taleb and he is the one that married Um Kalthoom daughter of Ali.”
Imam Ahmad Al-Hasan was once asked:
The Sunnis claim that Sayyida Um Kalthoom a.s was married to Umar and we are certain that it’s just a lie as it has been narrated that Umar bin Atheena said: I said to Abi Abdulah a.s: people argue with us and say: the Prince of Believers a.s gave his daughter Um Kalthoom to marry so-and-so, the Imam sat up and said: “Do they say this? the ones who claim this are people who do not guide to the straight path, subhanAllah wasn’t the Prince of Believers a.s capable of interfering to save her? they have lied and what they claimed didn’t happen…” -Bihar al-Anwar vol.42 p.88
They put forth this claim and ask if Umar wasn’t her husband, who was it then? So will you tell us, O master? By Allah our question is not out of doubt but we asked to increase in certitude.
Muhammad Shareef/Morocco
Imam Ahmed Al-Hasan answered:
“The husband of Um Kulthoom is Muhammad bin Jaafar bin Abi Talib, but may Allah have mercy upon you, you allow them to drag you to this? and what does this have to do with the truth and falsehood? wasn’t the wife of Pharaoh from the descendants of the prophets and she is one of the best women of the world as the prophet described her, wasn’t the wife of Noah and the wife of Lot disbelievers? And even if you said that her husband is so-and-so, will they be contented with what you said and would refrain from their fabrications?
If you want to overcome the people of conflict and fulfill the proofs on them, present the proof of the law of knowing the successor.”