Praise be to Allah.
Yes, if a Muslim has a regular practice of praying at night, but he sleeps and misses all of it or part of it, then it is recommended for him to make it up during the day. This was clearly narrated from the Prophet (blessings and peace of Allah be upon him).
Muslim (1779) narrated that ‘Umar ibn al-Khattab said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “Whoever sleeps and misses his regular portion of worship [prayers or reading Qur’an etc. that a person commits himself to do regularly] or part of it, then he recites it between Fajr prayer and Zuhr prayer, and it will be recorded for him as if he recited it at night.”
Shaykh Adam al-Ethiopi (may Allah have mercy on him) said:
What is meant is one who misses his entire regular practice of worship, or part of it, at night, because he is overcome by sleep.
We have interpreted it as referring to what is done at night, because that is what is indicated by the reference to sleep, and it is what is indicated by the end of the hadith, which says “as if he recited it at night”; and because of what it says in the following report: “Whoever misses his regular portion of worship at night.”
“Or any part of it” means any part of his regular portion of worship; in other words, if he misses part of his regular practice.
“Then he recites it between Fajr prayer and Zuhr prayer” may be understood as encouragement to hasten to make it up, or it may be understood as meaning that the reward for doing it will be multiplied, provided that it is made up at that particular time. This was stated by as-Sindi in Dhakheerat al-‘Uqba (18/175).
“or any part of it” means any part of his regular portion of worship, or part of his regular practice of reciting Qur’an or du‘a’s and dhikr. That also includes prayer (salah)."(Mirqat al-Mafatih 3/935).
Thus it becomes clear that if someone misses his regular practice, all of it or part of it, it is recommended for him to make it up during the day. So for one whose regular practice is to pray for two hours at night, and he only prays half an hour because of some excuse, it is prescribed for him to make up the other hour and a half during the day.
And Allah knows best.