What is the verse that the Prophet, peace and blessings be upon him, used to help him memorize the Qur’an, and through performing night prayers with which one of the Companions was able to memorize 40 at once?

Allah guaranteed His Prophet that He would preserve the Qur’an in his heart, as He, the Almighty, said: "Indeed, upon Us is its collection [in your heart] and [then] its recitation" (Quran 75:17), and "We will make you recite, [O Muhammad], and you will not forget" (Quran 87:6). There is no specific verse revealed to help with memorizing the Holy Qur’an. Furthermore, the narration transmitted about the Prophet’s — peace and blessings be upon him — teaching Ali — may Allah be pleased with him — what would help him memorize and master the Qur’an is a fabricated hadith.