Fiqh-us-Sunnah Volume 2, Supererogatory Prayer, Fiqh 2.143A.

Most of the people of knowledge are of the opinion that if a person catches only one rak’ah of al-Jumu’ah, then that rak’ah will be valid and the person need only make up the one rak’ah that he misses.

Ibn ‘Umar reports that the Prophet sallallahu alehi wasallam said: “Whoever catches only one rak’ah of the salah and then adds to it the other one, his prayer will be complete.” This is related by an-Nasa’i, Ibn Majah, and ad-Daraqutni. In Bulugh al-Maram, Ibn Hajar says that its chain is sahih although Abu Hatim says that the strongest opinion is that it is mursal.

Abu Hurairah reports that the Prophet sallallahu alehi wasallam said: “Whoever catches one rak’ah of the prayer has indeed caught the whole prayer.” This is related by the group.

Whoever catches less than one rak’ah of the salah has not caught the Jumu’ah and he is to pray four rak’at of the zuhr salah according to the majority of the scholars.

Ibn Mas’ud says: “Whoever catches one rak’ah from al-Jumu’ah is only to add another one to it. Whoever misses both rak’at is to pray four rak’at.” This is related by at-Tabarani with a good chain.

Ibn ‘Umar says: “If one catches from the Friday salah one rak’ah, then he is to add another one to it. If he catches only the sitting [at the end of the prayer, following the bowing], then he is to pray four [rak’at].” This is related by al-Baihaqi. Such is the opinion of the Shaf’i, Maliki, and Hanbali schools, and Muhammad ibn al-Hassan. Abu Hanifah and Abu Yusuf say that if one catches the tashahud with the imam, then he has caught al-Jumu’ah. He should pray two rak’at after the imam makes the taslim, and his Friday salah would be complete.