Sheikh Hamed Al-Ali, instructor of Islamic Heritage at the Faculty of Education, Kuwait and Imam of Dahiat As-Sabahiyya Mosque, states the following: As for Salatul-Jama`ah (congregational prayer), it is reached by joining the last Rukoo` (bowing). If one joins the Jama`ah in the last Rukoo` that means one has caught up with the Rak`ah and the Jama`ah.
As for Salatul-Jumu`ah (Friday Prayer), it is reached by joining one Rak`ah, even by joining the Salah while the Imam is still performing the second Rukoo` (i.e. in the second Rak`ah), then one has caught the Jumu`ah prayer. In this case one is supposed to pray one more Rak`ah and then finish his Salah.
However, if one joins the Salah while the Imam has already risen from the second Rukoo` , then one has missed the Jumu`ah. In this case he is supposed to assume the intention of praying Dhur and then join the Salah, then get up to pray four Rak`ahs after the Imam makes the Tasleem and finishes the Salah.
In his book Fiqh-us-Sunnah, the late Azharite scholar Sheikh Sayyed Sabiq, may Allah bless his soul, adds:Most scholars agree that if a person catches only one Rak`ah of Salatul-Jumu`ah, then that Rak`ah will be valid and the person needs only make up for the one Rak`ah that he misses.
Ibn `Umar, may Allah be pleased with him, quotes the Prophet (peace and blessings be upon him), as saying: “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 this Hadith’s chain of narration is Sahih (authentic) although Abu Hatim says that the strongest opinion is that it is Mursal (Hadith with a broken chain of narrators.) Abu Hurairah, may Allah be pleased with him, quotes the Prophet, peace and blessings be upon him, as saying: “Whoever catches one Rak`ah of the Friday prayer has indeed caught the whole prayer.” Whoever catches less than one Rak`ah of the Salah has not caught the Jumu`ah and he is to pray four Rak`ahs of the Dhur prayer according to the majority of scholars.
Ibn Mas’ud (may Allah be pleased with him) says: “Whoever catches one Rak`ah from the Jumu`ah is only to add another one to it, but whoever misses both Rak`ahs is to pray four Rak`ahs.” (This is related by At-Tabarani with a good chain of narrators.)
Ibn `Umar, may Allah be pleased with him, says: “If one catches one Rak`ah from the Jumu`ah, then he is to add another one to it. If he catches only the last sitting [at the end of the prayer, following the Rukoo` ], then he is to pray four [Rak`ahs].” This is related by Al-Baihaqi.
Such is the opinion of the Shaf’ie, Maliki, and Hanbali schools, and Muhammad Ibn Al-Hasan.
Abu Hanifah and Abu Yusuf say that if one catches the Tashah-hud with the Imam, then he has caught the Jumu`ah. He should pray two Rak`ahs after the Imam, makes the Tasleem, and his Jumu`ah would be complete.”
Thus, if you join the Jama`ah in the second Rukoo` in the Jumu`ah prayer, then your Jumu`ah is complete. But if you join the Jama`ah after the second Rukoo` then it is not counted as Jumu`ah and you should intend to pray Dhur and add four Rak`ahs.