Should one complete reciting Al-Fatiha or the Tashahhud, even if the Imam bows or stands for the third Rak'ah before their completion?

The congregant must follow the Imam in all his movements, and his action should be after the Imam, not with him or before him. It is prescribed for the congregant to lag slightly behind the Imam, so he should not begin moving until the Imam reaches the (next) pillar. Slight lagging behind the Imam, such as delaying the bowing to recite Al-Fatiha or delaying the Tashahhud, but still catching the Imam in the (next) pillar before he rises or moves, is contrary to the Sunnah but does not invalidate the prayer.