Whoever memorizes the holy book of Allah(swt) will be rewarded and honored greatly for that. He will rise in status in heaven to a level that commensurates with what he memorized from it.

Al-Tirmidhi (2914) and Abu Dawood (1464) narrated from ‘Abd-Allah(swt)( ibn ‘Amr that the Prophet (peace and blessings of Allah(swt) be upon him) said: “It will be said to the companion of the Qur'an: Recite and rise in status, recite as you used to recite in the world, for your status will be at the last verse that you recite.” This hadeeth was classed as saheeh by al-Albaani in al-Silsilah al-Saheehah, 5/218, no. 2240, after which he said:

By companion of Quraan, we mean the one who memorizes it by heart. Prophet Muhammad(saw) said, "the one who knows more Quran should lead the people in Prayer."

The differentiation in status in paradise will depend on how much a person has memorized the Holy Quran in this world.

The virtue of a Hafiz who has memorized Allah(swt)s book is subjected to a condition and that is he has memorized it for the sake of Allah(swt) and not for the worldly gains.

 Otherwise, the Prophet (peace and blessings of Allah(swt) be upon him) said: “Most of the hypocrites of my ummah are among those who have memorized Qur'an.”

 Narrated from ‘Aa’ishah - the Prophet (peace and blessings of Allah(swt) be upon him) said: “The likeness of the one who reads Qur'an and memorizes it is that he is with the righteous honorable scribes. The likeness of the one who reads it and tries hard to memorize it even though it is difficult for him, he will have two rewards.” Bukhari(4937)

Such is the virtue of a person who tries to memorize the book of Allah(swt).

For a person who has memorized the Quraan, praying qiyaam-al-layl is easy. The Quran will intercede for him on the day of Judgement. The Prophet (saw) said:

 Qur’aan will intercede for a person on the Day of Resurrection. Fasting will say, ‘O Lord, I deprived him of food and desires during the day, so let me intercede for him.’ The Qur'an will say, ‘O Lord I deprived him of his sleep at night, so let me intercede for him.’ Then they will both intercede for him.” Narrated by Ahmad, al-Tabaraani and al-Haakim; classed as saheeh by al-Albaani in Saheeh al-Jaami’, no. 3882
“Fasting and the

And Allah(swt)knows best.

It should be noted here that there is a weak (da’eef) hadeeth that is quoted concerning the virtue of memorizing Qur'an. This hadeeth says, “The bearer of the Qur'an, if he regards what it permits as halaal and what it forbids as haraam, he will intercede for ten of his family members on the Day of Resurrection, all of whom deserved to enter Hell.” This was narrated by al-Bayhaqi in Shu’ab al-Eemaan (The Branches of Faith) from Jaabir; it was classed as da’eef by al-Albaani in Da’eef al-Jaami’.

All these hadith account the virtue of memorizing the Quran and how it will benefit a person on the day of Ressurection. Believers must at least try to memorize Quran and encourage their children to do same. May Allah(swt) reward us for our endeavors.