Is the rak'ah counted for someone who enters the prayer while the imam is rising from bowing, and he has not said "Allahu Akbar"?

If a congregant joins while the Imam is in rukoo’ (bowing), there are three scenarios for them: 1. They say the opening takbeer (takbeerat al-ihram) while standing, then bow while the Imam is still bowing, thereby catching the rak'ah (unit of prayer). 2. They say the opening takbeer while the Imam is bowing, but they bow after the Imam has risen. In this case, they do not catch the rak'ah and must make it up. 3. They bow directly without saying the opening takbeer. In this case, their prayer is invalid.

The jurists have unanimously agreed that whoever catches the Imam in rukoo' has caught the rak'ah, based on the saying of the Prophet, peace be upon him: "Whoever catches the rukoo' has caught the rak'ah." This is also supported by the actions of a group of Companions, such as Ibn Mas'ud, Ibn 'Umar, and Zayd ibn Thabit.