Is there any proof in the Sunnah that there is a prayer on the last Friday in Ramadan in expiation for the sin of one who missed the obligatory prayers?
Whoever omits an obligatory prayer until the time for it has ended, one of the following must be the case: either he omitted it for a legitimate reason such as falling asleep or forgetting, or he omitted it without any excuse. If a person omits it with for legitimate reason, there is no sin on him, but he must offer it when he wakes up or remembers. If a person omits it deliberately, then he has committed a grave sin and he must make it up according to many scholars; others favoured the view that he cannot make it up, but he is required to repent, pray for forgiveness, regret it, and do a lot of righteous deeds.
Please see the answer to question no. 13664
The report that speaks of a prayer that may be offered by one who omitted a prayer deliberately until the time for it ended, so that it may be an expiation for his deeds, is a lie and is falsely attributed to Islamic teaching. There follow some comments of the scholars concerning that:
1.Ash-Shawkaani (may Allah have mercy on him) said:
The hadeeth “Whoever prays the five obligatory prayers of the night and day on the last Friday of Ramadan, that will make up for what he missed of prayers during that year” is undoubtedly mawdoo‘ (fabricated). I could not find it in any of the books in which the authors compiled fabricated hadeeths, but it is well-known among a group of people who claim to have knowledge in the city of San‘aa’ nowadays, and many of them do that! I do not know who fabricated it and told it to them; may Allah curse the liars.
End quote from al-Ahaadeeth al-Mawdoo‘ah (p. 54)
2.The scholars of the Standing Committee for Issuing Fatwas said:
Prayer is an act of worship and the basic principle concerning it is tawqeef i.e., stopping at what has been narrated in sharee‘ah (and not introducing anything new); the issue of making up the prayers and details of how to do that is something to be learned from textsand it is not valid to refer to anything in this regard except the Book of Allah, the Sunnah of His Messenger (blessings and peace of Allah be upon him) and the consensus based on both of them or one of them. There is no proof from the Prophet (blessings and peace of Allah be upon him), or from his Companions (may Allah be pleased with them), or from the leaders of guidance (may Allah have mercy on them) that they offered this prayer or instructed or encouraged others to do so. If it was something established, then his Companions (may Allah be pleased with them) would have known about it and would have transmitted it to us, and the leaders of guidance after them would have guided us to it. But there is no proof to that effect from any of them in word or in deed. That indicates that what is mentioned in the question about the “prayer to make up for the prayers of a lifetime (salaat al-qada’ al-‘umri)” is a bid‘ah that has been introduced into Islam for which Allah has not prescribed. It is proven from the Prophet (blessings and peace of Allah be upon him) that he said: “Whoever introduces anything into this matter of ours that is not part of it will have it rejected.” (Agreed upon). Rather what the Messenger of Allah (blessings and peace of Allah be upon him) instructed us to do is to make up the prayers that one misses because of falling asleep or forgetting until the time for them ends, and he explained to us that we should offer those prayers as they are usually offered when we wake up or remember, not on the last Friday of Ramadan.
End quote from Fataawa al-Lajnah ad-Daa’imah (8/167, 168)
Shaykh ‘Abd al-‘Azeez ibn Baaz, Shaykh ‘Abd ar-Razzaaq ‘Afeefi, Shaykh ‘Abdullah ibn Ghadyaan, Shaykh ‘Abdullah ibn Qa‘ood
3.Shaykh Muhammad ibn Saalih al-‘Uthaymeen (may Allah have mercy on him) was asked:
There is a group of people who have a custom in Ramadan, which is to offer the five obligatory prayers after a prayer on the last Friday (of Ramadan), and they say that this is to make up for any obligatory prayers that a person did not offer or that he forgot in Ramadan. What is the ruling on this prayer?
The ruling concerning this prayer is that it is an innovation (bid‘ah) and it has no basis in Islamic teachings; it will only take a person further away from his Lord, because the Messenger of Allah (blessings and peace of Allah be upon him) said: “Every innovation is misguidance, and every misguidance will be in the Fire.” No matter how much the followers of an innovation like it and regard it as good in their own minds, it is something bad before Allah, may He be glorified and exalted, because His Prophet (blessings and peace of Allah be upon him) said: “Every innovation is misguidance, and every misguidance will be in the Fire.” These five daily prayers that a person makes up on the last Friday of Ramadan have no basis in Islamic teaching. Moreover, we say: has this person missed only five prayers? Perhaps he missed a number of days, not a number of prayers?
What matters is that so long as a person is aware that he has missed prayers, he must make them up when he realises that, because the Prophet (blessings and peace of Allah be upon him) said: “Whoever sleeps and misses a prayer or forgets it, let him off it when he remembers it” (Agreed upon). But if a person does these five prayers to be on the safe side – as they claim – that is something reprehensible and is not permitted.
End quote from Majmoo‘ Fataawa ash-Shaykh al-‘Uthaymeen (12/227, 228)
4.Shaykh Saalih al-Fawzaan (may Allah preserve him) was asked:
I read a hadeeth from the Messenger (blessings and peace of Allah be upon him) in which he said: “Whoever misses a prayer during his life and cannot remember what it was, let him get up on the last Friday of Ramadan and pray four rak‘ahs with one tashahhud, reciting in each rak‘ah the Opening of the Book (i.e., al-Faatihah) and Soorat al-Qadr fifteen times, and Soorat al-Kawthar the same number of times, and let him say in his intention: I intend to pray four rak‘ahs as expiation for what I have missed of prayers.” How sound is this hadeeth?
There is no basis for this in the Sunnah of the Messenger (blessings and peace of Allah be upon him). What is proven from the Messenger (blessings and peace of Allah be upon him) is that he said: “Whoever forgets a prayer or sleeps and misses it, let him offer it when he remembers it. There is no expiation for that except this” (agreed upon). With regard to the prayers that you missed previously, if you missed them because of sleep – for example – or because you were unconscious, or for some excuse that you thought made it permissible for you to delay them, then what you must do is make them up and offer them in order. If you missed them deliberately, then the more correct of the two scholarly views is that you must repent to Allah, because the one who misses prayer deliberately is in a grave position, even if he does not deny that they are obligatory. The correct view is that he has become a disbeliever by doing that. So you must repent to Allah if you missed them deliberately, and you must persist in offering prayers regularly in the future, and may Allah accept your repentance.
But if you missed them because of sleep or unconsciousness, or something else that prevented you from offering them on time, then you have no choice but to make them up. As for offering this prayer that you mentioned at the end of Ramadan in this manner, there is no basis for that in Islamic religion, and it will not make up for the prayers that you missed. End quote.
For more information please see the answer to question no. 49612
And Allah knows best.