The greeting of the mosque is a recommended practice that is not made up
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Q: What is the ruling on one who performs two rak'ahs after the Fajr prayer? Is it obligatory for one who missed the greeting of the mosque before the prayer? And when is its time?
A: The greeting of the mosque is a recommended practice (sunnah); it is not made up, and it is dropped from the Muslim if he enters while they are praying, and the obligatory prayer suffices for him. If he did not pray the regular voluntary prayer at home—that is, the sunnah of Fajr—and he arrives and the imam has already entered the prayer, then he has a choice: if he wishes, he prays it after the prayer, and if he wishes, he prays it after the sun has risen, as that is established from the Prophet (peace and blessings be upon him). However, if he arrives and the imam has not yet started the prayer, he prays the regular voluntary prayer, and it suffices him for the greeting of the mosque.
A: The greeting of the mosque is a recommended practice (sunnah); it is not made up, and it is dropped from the Muslim if he enters while they are praying, and the obligatory prayer suffices for him. If he did not pray the regular voluntary prayer at home—that is, the sunnah of Fajr—and he arrives and the imam has already entered the prayer, then he has a choice: if he wishes, he prays it after the prayer, and if he wishes, he prays it after the sun has risen, as that is established from the Prophet (peace and blessings be upon him). However, if he arrives and the imam has not yet started the prayer, he prays the regular voluntary prayer, and it suffices him for the greeting of the mosque.
Source
binbaz.org.sa
The Arabic text is copied verbatim from the original source, without any edits.