Takbeer of movement (changing posture) for one who joins the congregation when the imam is bowing or prostrating

If (a person) comes when the people are bowing, what he
must do first is say the takbeer for starting to pray (takbeerat
al-ihraam), then if he can, he should say the takbeer for bowing whilst
leaning forward; if he cannot do that, then the takbeerat al-ihraam will
suffice, according to the correct scholarly view.  But if he does both,
that is better and more perfect, and will avoid a matter concerning which
the scholars differed. Then he should bow with the imam and this rak‘ah
will be valid for him and he does not have to make it up. 

But if he comes when they are prostrating, he should say
takbeerat al-ihraam only whilst standing, then go down in prostration
without saying the takbeer, and this rak‘ah will not count for him, because
he missed standing and bowing with them. End quote. 

Shaykh ‘Abd al-‘Azeez ibn Baaz (may Allah have mercy on him)