She stipulated that in order to marry her he has to memorize Soorat al-Baqarah or Aal ‘Imraan or take her for Hajj

Praise be to Allah.

If you want to marry her because she is religiously committed and you agree to the condition, seeking thereby the pleasure of Allah and to achieve this aim, and to marry someone who will help you to obey Allah and you can help her, then there is nothing wrong with that and this is part of striving for the Hereafter. Allah says (interpretation of the meaning):

“And whoever desires the Hereafter and strives for it, with the necessary effort due for it (i.e. does righteous deeds of Allaah’s obedience) while he is a believer (in the Oneness of Allaah Islâmic Monotheism) — then such are the ones whose striving shall be appreciated, (thanked and rewarded by Allaah)”

[al-Isra’ 17:19]. 

Al-Nasaa’i (3340) narrated that Anas (may Allah be pleased with him) said: Abu Talhah married Umm Sulaym and the dowry between them was Islam; Umm Sulaym became Muslim before Abu Talhah. He proposed to her and she said: I have become Muslim; if you become Muslim I will marry you. So he became Muslim, and that was the dowry between them. Classed as saheeh by al-Albaani in Saheeh al-Nasaa’i. 

So strive to memorise the Holy Qur’aan as an act of worship and obedience towards Allah, and seeking His reward and His pleasure. There is no reason not to let the request of this sister be what motivates you to do this act of worship, because it is not contrary to sincerity. This is like those who enter some religious competitions and let that a motive to memorise the Holy Qur’aan. So there is nothing wrong with that and it is not contrary to sincerity. 

The scholars of the Standing Committee for Issuing Fatwas were asked: Taking part in religious competitions that offer cash prizes: are these prizes halaal or haraam? 

They replied: There is nothing wrong with accepting the prizes that are donated by people in authority or other doers of good, because that is encouragement to acquire knowledge and memorise the Book of Allah, may He be glorified and exalted. In these and similar matters, the believer should be sincere towards Allah and be happy to have something that helps him in that, and his motivation should not be only to get the money. End quote. 

Fataawa al-Lajnah al-Daa’imah, 15/188                         

And Allah knows best.