Is the prayer valid for someone who catches the Imam bowing, then says the opening "Allahu Akbar," and then incorporates the "Allahu Akbar" for bowing into it?

If a worshiper joins the Imam while he is bowing, the first takbir (the opening takbir or takbirat al-ihram) is sufficient, according to a group of scholars, because it is the greatest pillar without which the prayer cannot be established. As for the takbir for bowing, some have said it is obligatory, while others have said it is a sunnah (recommended act), and it is of lesser importance than the first takbir. If time is constrained, the first takbir suffices for the takbir for bowing. The best approach is to combine both: perform the takbirat al-ihram while standing, and then perform the takbir for bowing while descending into the bowing position. However, if one limits himself to the takbirat al-ihram, that is sufficient.