How does a Muslim make up the prayers he missed?

Q: How does a Muslim make up the prayers he missed, such as the Fajr prayer, for example? And if the prayer is one in which the recitation is loud, is it obligatory for him to recite loudly when making it up? Please inform us, may Allah reward you.

A: It is obligatory for one who has obligatory prayers upon him to hasten to make them up just as if he were performing them in their time. If they are prayers with loud recitation, he makes them up with loud recitation, such as Fajr, 'Isha', and Maghrib. If they are prayers with quiet recitation, he makes them up with quiet recitation, such as Zuhr and 'Asr. He makes them up just as he performs them in their time. This is if he left them off due to forgetfulness, or sleep, or a doubtful illness where he claimed he could not perform them while ill, so he delayed them out of ignorance. In this case, he makes them up as they were, based on the saying of the Prophet (peace and blessings be upon him): It is agreed upon that it is authentic.
It is also authentic that he (peace and blessings be upon him) slept through the Fajr prayer on one of his journeys, along with his Companions, and nothing woke them up but the heat of the sun. When they woke up, he (peace and blessings be upon him) ordered Bilal to give the call to prayer, and they prayed it, just as they would have prayed it in its time.
As for if he left it off intentionally, and then Allah guided him and he repented, he does not have to make it up. This is because leaving it off intentionally is major shirk (associating partners with Allah). So if he repents to Allah from that, he does not have to make it up, because repentance erases what came before it. If the servant repents with a sincere repentance from leaving off the prayer, Allah erases what he left off for him by that, and he does not have to make it up, according to the stronger of the two opinions of the scholars.
Making up the prayer is only for the one who left it off due to forgetfulness, or out of his ignorance of the obligation of performing it because of an illness that struck him, so he wanted to delay it until he could pray it while healthy, or because of sleep. This is the one who makes it up. As for the one who leaves it off intentionally—may we seek refuge in Allah from that—he commits kufr (disbelief) by that, based on the saying of the Prophet (peace and blessings be upon him): It was narrated by Imam Ahmad and the people of the Sunan with an authentic chain, from Buraydah ibn al-Husayb al-Aslami (may Allah be pleased with him). And he (peace and blessings be upon him) said: It was narrated by Imam Muslim in his Sahih, from the hadith of Jabir ibn 'Abdullah (may Allah be pleased with them both). There are other hadiths in this chapter that indicate this.
The summary is that if he leaves it off intentionally, either out of negligence toward it or denial of its obligation, he commits kufr. If he is one who denies its obligation, he commits kufr by consensus. The scholars have agreed that one who denies the obligation of prayer commits major kufr. We ask Allah for safety. But if he leaves it off out of negligence and laziness, he has resembled the hypocrites, and that is major kufr according to the stronger of the two opinions of the scholars.
So he must repent to Allah—sincere, earnest repentance—which includes: regret for what has passed, abandoning it, and resolving not to return to such a thing; out of reverence for Allah (Glorified and Exalted is He), desire for His reward, and fear of His punishment. And he does not have to make up the prayers, because the Prophet (peace and blessings be upon him) did not order the one who apostatized from Islam and then repented to make up the prayers he left off. Likewise, his Companions (may Allah be pleased with them) in the time of al-Siddiq and after him did not order the apostates to make up the prayers they had left off. And he (peace and blessings be upon him) said: And he (peace and blessings be upon him) said: .
And success is from Allah.