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

                If I come when the congregation is bowing or prostrating, is it sufficient for me to say the takbeer for bowing or prostrating, or do I have to say the takbeer for ihraam (starting the prayer), then follow it with the takbeer for bowing or prostrating?
Praise be to Allah.
      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)