Is it permissible to offer the prayer in congregation after the prayer time has elapsed, like, for example, offering the Fajr prayer after sunrise?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.

It is not permissible for the Muslim to postpone offering the prayer after its due time; Allaah The Almighty Says (what means): {Indeed, prayer has been decreed upon the believers a decree of specified times.}[Quran 4: 103 ]

Jibreel, may Allaah Exalt his mention, explained to the Messenger of Allaah, sallallaahu ‘alayhi wa sallam, the beginning and end of the time of each prayer. Therefore, it is not permissible for any Muslim to advance or delay offering the prayer.

However, if the individual experienced any matter that prevented him from offering the prayer in its due time, he must make up for it according to the same form of offering it in the due time. Hence, there is no difference between the two cases. So, he may offer it in congregation if there are other people in the same condition. It was authentically reported that one day the Messenger of Allaah, sallallaahu ‘alayhi wa sallam, and his Companions slept while travelling and did not wake up until after the sun had risen [Al-Bukhari and Muslim], so they offered the regular voluntary prayer and then offered the Fajr prayer [Abu Daawood]. In the narration of Saheeh Muslim, he, sallallaahu ‘alayhi wa sallam, did what he used to do every day.

Thus, this story signifies that the form of the made up prayer is the same of the offered prayer with no difference.