Is it permissible to make up missed prayers during the prohibited times, and what is the recommended practice?

For example, if a person wakes up for the Fajr prayer when the sun has risen, the Messenger (peace and blessings be upon him) said that this is the time for that forgotten prayer. A man who forgot the 'Asr prayer until the sun was about to set, or had set, prays it even if the time is one in which prayer is disliked and prohibited. There are many, and very many, specific exceptions. Abu al-Tayyib al-Hindi did well in his book titled "Informing the People of the Era of the Rulings on the Two Rak'ahs of the Fajr Sunnah," where he collected the hadiths that specify the times in which prayer is prohibited. Among these was what I mentioned earlier: the forgotten prayer. From what comes to my mind is the prayer of one who prayed Fajr in his home, then went to the mosque and found them praying; he prays with them even if the prayer after his own is in a time when prayer is prohibited. And so on. If we specify the hadiths prohibiting prayer in the known times with the hadith , because these hadiths prohibiting prayer have been subjected to specification, and this means that their generality is weakened, whereas the generality of the hadith , since it was not specified, remains in its comprehensive, absolute generality. It is possible to apply this absolute generality to that specified generality, and the result is: no prayer after 'Asr, no prayer after Fajr, except for the greeting of the mosque, due to that generality which was not subjected to specification. This is the first point.
The second point, which I mentioned, is an argument by stronger analogy. You all know, if Allah wills, that the Prophet (peace and blessings be upon him) . Listen, O Shaykh, . Prayer while the imam is delivering the sermon is prohibited; voluntary prayer is prohibited. So, when we find that the Messenger (peace and blessings be upon him) commanded the greeting prayer in this time when voluntary prayer is generally prohibited, we take from this an indication that the greeting prayer is performed in the times when prayer is prohibited. This is a time in which prayer is prohibited. In reality, this is a point of jurisprudence that was not mentioned in the books of jurisprudence. When the books of jurisprudence mention the times in which prayer is disliked, they do not mention the time when the imam is delivering the sermon as one of the times in which prayer is disliked. Therefore, there are two benefits here: the first benefit is that it is recommended to add the time when the imam is delivering the sermon to the times in which prayer is disliked. The second benefit is that this time, in which prayer is prohibited, is utilized to permit the greeting prayer in the other times in which prayer is disliked, based on the evidence that the Messenger (peace and blessings be upon him) said: This is the answer to the previous question.

The questioner : Is the hadith regarding the two rak'ahs of the greeting of the mosque, in general, considered specified by the hadith of the Prophet (peace and blessings be upon him) ?

The Shaykh : And what is the meaning of my previous statement?

The questioner : I mean, you said that general prayers are not recommended except for the greeting of the mosque.

The Shaykh : Did I say "except"? I did not say "except," my brother. I said the opposite. I said that these times in which prayer is prohibited have many specific exceptions, which Abu al-Tayyib al-Hindi collected in the aforementioned book. I mentioned some examples for the sake of approximation. So, did this "except" come out of your pocket, O Wafi'?!

The questioner : Our Shaykh, I mean, after a person has prayed Fajr with the congregation in the mosque, the one who prayed the congregation prays...?

The Shaykh : It is permissible, for others.