All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
The jurists agreed on the excellence of memorizing the Quran, but they do not consider it as being obligatory. However, a mature, sound Muslim should at least learn Surah Al-Faatihah (the Opening Chapter of the Quran) because the prayer is invalid without it.
The person who does not memorize the whole Quran is not sinful, and his fate is not to hell if he dies without memorizing it. However, many Ahadeeth encourage memorizing the Quran.
Among these Ahadeeth is the saying of the Prophet : “The best people amongst yourselves are those who study the Quran and teach it (to others).” [Al-Bukhari]
‘Umar narrated that the Prophet said: “Indeed Allah raises in status people with the Quran, and diminishes the status of others because of it.” [Muslim]
Besides, Ibn ‘Umar narrated that the Prophet said: “There is no envy except in two (cases): A man whom Allah has taught the Quran and he recites it during the hours of the night and during the hours of the day, and another man listens to him and says, 'I wish I had been given what has been given to so-and-so, so that I might do what he does'; and a man whom Allah has given wealth and he spends it on what is just and right. Whereupon another man may say, 'I wish I had been given what so-and-so has been given, for then I would do what he does.” [Al-Bukhari and Muslim]
Moreover, Ibn ‘Abbaas narrated that the Prophet said: “A person who does not memorize anything from the Quran is like a damaged or destroyed house.” [At-Tirmithi]
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Allah knows best.