Mention of Musaylimah the Liar and his claim to prophethood

Al-Qasim bin Abd al-Rahman narrates from his father that a man came to Sayyiduna Abdullah bin Mas'ud (may Allah be pleased with him) and said: "O Abu Abd al-Rahman! There are some people here who recite according to the recitation of Musaylimah (the Liar)." Abdullah said: "Can there be, after Islam has spread, any book other than the Book of Allah, or any messenger other than the Messenger of Allah?" He sent him back. The man came again and said: "O Abdullah! By the One besides whom there is no god, they are in that house reciting the recitation of Musaylimah, and they have with them a mushaf in which the words of Musaylimah are written." This was during the caliphate of Sayyiduna Uthman (may Allah be pleased with him). Abdullah said to Qarazah, who was the head of the cavalry: "Go and surround that house and bring those who are in it." He did so and brought eighty men. Abdullah said to them: "Woe to you! Is there any book other than the Book of Allah, or any messenger other than the Messenger of Allah?" They said: "We repent to Allah; we have wronged ourselves." So Abdullah let them go and did not fight them; rather he exiled them to Syria, except their ringleader Ibn al-Nawwahah, who refused to repent. Then Abdullah said to Qarazah: "Go and strike off his neck and throw his head into his mother's lap, for I think his mother knew of this deed of his." So he did so. Then Abdullah began narrating and said: "This man (Ibn al-Nawwahah) and Ibn Uthal came as messengers from Musaylimah to the Messenger of Allah (peace and blessings be upon him). The Messenger of Allah (peace and blessings be upon him) asked him: 'Do you bear witness that I am the Messenger of Allah?' He retorted to the Messenger of Allah (peace and blessings be upon him): 'Do you bear witness that Musaylimah is the messenger of Allah?' The Messenger of Allah (peace and blessings be upon him) said: 'Were you not a messenger, I would have killed you.' And from that day the sunnah was established that a messenger is not killed."
This hadith has an authentic (sahih) chain of narration, but the two Shaykhs (Bukhari and Muslim) did not record it.

It is narrated from Sayyiduna Anas (may Allah be pleased with him) that the Messenger of Allah (peace and blessings be upon him) met Musaylimah (the Liar), and Musaylimah said to him: "Do you bear witness that I am the messenger of Allah?" The Messenger of Allah (peace and blessings be upon him) said: "I believe in Allah and His messengers." Then the Messenger of Allah (peace and blessings be upon him) said: "This is a man who has been left behind for the destruction of his people."
This hadith has an authentic (sahih) chain of narration, but the two Shaykhs (Bukhari and Muslim) did not record it.