How to make up missed prayers: are they made up in order, or is each obligatory prayer made up with its corresponding prayer?

Question:
The first message in this episode is from Yemen, Hajjah Governorate, sent by one of the listening brothers there. He asks a number of questions; in one of them he says: I would like an answer, if you would be so kind, regarding making up missed prayers. Is there a requirement to make up missed prayers? And how are they made up? Are they made up all at once? Or is each obligatory prayer made up with its corresponding prayer? That is, the Fajr prayer with Fajr, the Zuhr prayer with Zuhr, and so on? Please give us a ruling, may Allah reward you with good.

Answer:
In the name of Allah, the Most Gracious, the Most Merciful. All praise is due to Allah, Lord of the worlds, and may Allah send prayers and blessings upon our Prophet Muhammad, and upon his family and all his Companions. As for what follows, prayer is the second pillar of the pillars of Islam after the two testimonies, and it is the pillar of Islam. There is no religion for one who does not pray, and there is no Islam for one who does not pray. Therefore, it is obligatory to perform it in the times in which Allah the Exalted has prescribed it. He the Exalted said: meaning that it is obligatory in its times.
Allah and His Messenger have designated specific times for each prayer in which it is to be performed, and it is not permissible to perform it outside of that time except for a valid legal excuse. If a person forgets a prayer until its time has passed, or sleeps through it due to an occasional sleep until its time has passed, then it is obligatory for him to make it up, and to hasten in making it up, based on the saying of the Prophet (peace and blessings be upon him): If a person has several prayers that he has missed, it is obligatory for him to make them up immediately in order, and he should not delay each prayer to be made up with its corresponding prayer, as some people think. Rather, he should pray them all in one time, with quick haste as much as he is able, and arrange them: he prays Fajr, then Zuhr, then 'Asr, then Maghrib, then 'Isha' for the first day, then he starts again with Fajr, then Zuhr, then 'Asr, then Maghrib, then 'Isha' for the second day, and so on, until he completes what is due from him. If it happens that there are many prayers that require a long time, and he is unable to recite them all in sequence, then he makes up what he can in one period, and delays the rest to another period according to his ability and capacity. This is what is obligatory for the Muslim if he misses a prayer or multiple prayers; he must make them up, because they are a right that is obligatory and a debt in his liability, which he must perform in its time or make up if its time has passed. And success is from Allah.