Joining The Congregational Prayer Late

If one joins the congregational prayer late ( 3rd or 4th rakah) what is the proper way to complete the prayer? in Which rakah he has to recite a surah and in which rakah he has to sit after Sajdah?

A person who has not joined a prayer in the first rakah is called a ‘Masbuq’. He has to complete his prayer after the Imam has finished his prayer. A ‘Masbuq’ has to observe the following rules while completing his prayer :-
1. He should not make salam with his Imam ; rather as soon as Imam completes his first Salam he should stand up to complete his prayer.
2. By completing his own prayer, a ‘Masbuq’ shall perform all the acts of prayers in the same manner as he has to perform while praying individually.
3. In the matter of recitation of surah he shall follow his own number of rakah i.e. if he has missed two rakah with the Imam and has stood up to complete these remaining rakah, he will have to recite surah in both of them because these rakah will be deemed to be his first and second rakah and his performance with the Imam will be deemed to be third and fourth. Likewise, if he has missed three rakah and performed only one rakah with the Imam, then while performing the remaining three rakah, he will recite surah in the first two rakah only and will not recite in the third.
4. However, in the matter of Qa’dah (sitting for Tashahhud), he will follow the number of rakah he has actually perfor med whether with the Imam or on his own. Therefore, if he has missed three rakah and has performed only one rakah with the Imam, then he will have to sit for Qa’dah right in the first rakah whike completing his own prayer, because this is actually his second rakah as combined with the one performed with the Imam, and since Qa’dah is obligatory after every two rakah he has two make Qa’dah right there and he will not sit in the next rakah because it is actually his third rakah.
In the light of aforesaid rules, if a person has missed three rakah and joined only in the fourth rakah with the Imam, he will not follow the Imam in his salam and will stand up to complete his remaining three rakah and in the first rakah will recite surah and after completing sajdah he will sit down to recite tashahhud, then he will rise up and will recite the surah again. He will not sit in this second individual rakah. Then in the third, he will not recite a surah and will sit down after sajdah to complete his Tashahhud and salam.
I hope this will be enough to explain the way in which a ‘Masbuq’ has to complete his prayer.

Fatawa by Mufti Muhammad Taqi Usmani.