Reference: http://binothaimeen.net/content/6642
َQuestion: He [was] ill and underwent surgery, and [during this time] he missed a number of obligatory prayers; so should he pray them all together once he is better, or should he pray each obligatory prayer at its time, such as ‘asr at the time of ‘asr, and zhuhr at the time of zhuhr, and maghrib at the time of maghrib…and so on?
Response: He should pray them all together at the same time; that is because when the Prophet ﷺ missed the ‘asr prayer during the battle of Khandaq, he prayed it [promptly upon remembering] before the maghrib prayer. Like this [therefore], it is obligatory upon anyone who has missed a[ny obligatory] prayer[s] to pray them promptly, and together – without any delay.
Question: And in reality, many people ask about this, as it is a cause of much confusion. That is because it appears to them that each prayer [which needs to be made up] should be prayed at its time, so [the] zhuhr [prayer which needs to be made up] should be delayed until the time of zhuhr; and like this, a whole day will pass without [him making up that missed] prayer.
Response: And this [understanding] is wrong. That is because the time for making up the [missed] obligatory prayers is the moment he remembers them, [and this is] based upon the saying of the Prophet ﷺ:
«Whoever forgets a prayer or sleeps and misses it, its expiation is to make it up as soon as he remembers it» [transmitted by Muslim]