We have discussed this shia claim previously, just additional information from brother Saad (hafizahullah):
‘Allamah Sarfaraz Khan Safdar mentions in Khazain al-Sunan, 1:99, that the claim that Sayyiduna ibn Masu’d (may Allah be pleased with him) didn’t consider Muawidhatayn to be part of the Qur’an is an outright lie.Mufti Muhammad Sa’eed Khan mentioned that there are authentic proofs which show that Ibn Masu’d considered Muawidhatayn to be part of the Qur’an. How could he not? To deny one letter of the Qur’an iskufr, let alone two whole Surahs of the Qur’an. Mufti Zar Wali Khan mentioned that it is proven that he recited the Muawidhatayn in prayer.
Also, there is an interesting discussion by Dr. Muhammad Muftasa al-A’zami in The History of the Qur’anic Text from Revelation to Compilation. He also discusses why the opinion of Hafiz ibn Hajr is rejected and his error in the light of muhaddithin’s methodology. See p.201.