ALLAAH is the KING of the Heavens & the Earth
For new Muslims ALLAAH’s Messenger (peace on him) granted some concession to them, but they (new Muslims) should also learn Qur’an and they should not solely depend on these concession.
(I) This is for him who just become Muslim and knew nothing Qur’an by heart
Rifa`ah bin Rafi` narrated:
“One day Allah’s Messenger was sitting in the Masjid” Rifa’ah said: “And we were with him. ……. Go back and perform Salat, for indeed you have not prayed.’ – until the people got scared and became very worried that one whose prayer was so brief had not actually prayed. Then in the end the man said: ‘Then show me, and teach me, for I am a human who has suffered and is mistaken.’ So he said: ‘Alright. When you stand for Salat then perform Wudu as Allah ordered you. Then say the Tashahhud, and the Iqamah as well. If you know any Quran then recite it, if not then praise Allah(Alhamdulillah), mention His greatness(ALLAAH u Akbar), and the Tahlil(la ilaha illa ALLAAH). Then bow such that you are at rest in your bowing, …
Reference : Jami` at-Tirmidhi 302
(2) He(New Muslim) should learn Qur’an and can recite whatever he learned
Narrated Abu Huraira:Once the Prophet (ﷺ) entered the mosque, a man came in, offered the prayer and greeted the Prophet. …. Kindly teach Me how to pray.” He said, “When you stand for the prayer, say Takbir and then recite from the Qur’an what you know and then bow with calmness till you feel at ease, then rise from bowing till you stand straight. Afterwards prostrate calmly till you feel at ease and then raise (your head) and sit with Calmness till you feel at ease and then prostrate with calmness till you feel at ease in prostration and do the same in the whole of your prayer.”
Sahih al-Bukhari 793
(3) He(New Muslim) should learn Qur’an and can recite whatever is easy for him.
It was narrated from Abu Hurairah that:
The Messenger of Allah (ﷺ) entered the Masjid, then a man entered and prayed, then he came and greeted the Messenger of Allah (ﷺ) with Salam. The Messenger of Allah (ﷺ) returned his greeting and said: Go back and pray, for you have not prayed.” So he went back and prayed as he has prayed before, then he came to the Prophet (ﷺ) and greeted him with Salam, and the Messenger of Allah (ﷺ) said to him: “Wa alaika as-salam (and upon you be peace). Go back and pray for you have not prayed.” He did that three times, then the man said: “By the One Who sent you with the truth, I cannot do any better than that; teach me.” He said: “When you stand to pray, say the Takbir, then recite whatever is easy for you of Quran. Then bow until you have tranquility in your bowing, then stand up until you are standing straight. Then prostrate until you have tranquility in your prostration, then sit up until you have tranquility in your sitting. Then do that throughout your entire prayer.”
Sunan an-Nasa’i : Hadith 885
ALLAAH knows best