Recitation in prayer is obligatory on the imam and the follower, and those who waived recitation for the latecomer in the first rakah only

It is narrated from Sayyiduna Abu Hurayrah (may Allah be pleased with him) that he said: "Whoever catches the congregation while they are bowing, that rak'ah of his (in which he caught only the bowing) will not be counted."
Imam al-Bayhaqi recorded this narration in al-Sunan al-Kubra, and its chain is hasan (good). It is a mawquf statement (athar) of Sayyiduna Abu Hurayrah (may Allah be pleased with him), from which it is understood that in his view the rak'ah is not caught by catching the bowing; rather, catching the standing is necessary.

It is narrated from an elder of the Ansar that a man entered the mosque, and the Messenger of Allah (peace and blessings be upon him) heard the sound of his sandals. When he (peace and blessings be upon him) had said the salam of the prayer, he asked him: "In what state did you find us?" He said: "You were in prostration, so I also prostrated." He (peace and blessings be upon him) said: "Do it like that, and do not count the prostration alone (as a rak'ah) until you have caught the complete rak'ah (with the bowing). So when you see the imam standing, stand; when you see him bowing, bow; when you see him prostrating, prostrate; and when you see him sitting, sit."
This hadith is sahih (authentic).