When should the takbeeraat of movement be said during the prayer?
Question

When the imam is praying, when should he say takbeer for bowing, for example? Should he say takbeer before he bows, whilst bowing or after bowing?.
Praise be to Allah.What is prescribed for everyone who prays (the imam, the one who is praying behind the imam and the one who is praying alone) is for the takbeer for bowing to accompany the movement. So he should start saying takbeer when he starts to bow, and end it before he reaches the bowing position, so that his takbeer comes between the two postures of standing and bowing. 
The Sunnah indicates that the takbeer should accompany the intended movement such as bowing, prostrating and standing up. It is narrated in al-Saheehayn that Abu Hurayrah (may Allah have mercy on him) said: When the Messenger of Allah (S) stood up to pray, he would say takbeer when he stood up, then he would say takbeer when he bowed, then he would say “Sami’a Allahu liman hamidah (Allah hears those who praise Him)” until he was standing up straight after bowing, and when he was standing he would say, “Rabbana wa laka’l-hamd (our Lord, to You be praise).” Then he would say takbeer when he went down in prostration, then he would say takbeer when he raised his head, then he would say takbeer when he prostrated, then he would say takbeer when he raised his head, and he did that throughout the prayer until he finished. And he would say takbeer when he stood up after two rak’ahs, after sitting.” 
Narrated by al-Bukhaari (789) and Muslim (392). 
This hadeeth shows that the takbeer for bowing should be said whilst bending down to bow, and the takbeer for prostration should be said when going down for prostration, and the takbeer for standing up from prostration should be said whilst rising, and so on. This was stated by al-Nawawi in Sharh Muslim, and he said that it is the view of the majority of scholars. 
Some of the fuqaha’ were very strict on this point, and said that if the worshipper starts to say the takbeer when he is standing, before he bends down, or he completes it after he reaches the bowing posture, that does not count and he has failed to say takbeer properly, because he has not done it at the right time. According to the view that takbeer is obligatory, he has invalidated his prayer if he did that deliberately, and if he did it by mistake he must perform the prostration of forgetfulness (sujood al-sahw). The correct view, however, is that this is forgivable, so as to avoid undue hardship. 
Al-Mardaawi said in al-Insaaf (2/59): Majd and others said: The takbeer for going down and rising and standing up should start when the movement begins and end when it ends. If he completes it partway through, that is sufficient [i.e., if it happens between the two postures without elongating it], because it has not been done at the wrong time. There is no scholarly difference of opinion on this matter. 
But if he starts it before that or ends it after that, and some of it happens outside the proper place, then this is like not doing it at all, because he did not complete it at the right time. It is like one who completes his recitation whilst bowing, or who starts to recite the tashahhud before sitting. 
But he may be forgiven for that, because avoiding it is difficult, and mistakes are often made, and it is too harsh to suggest that this invalidates the prayer or requires the prostration of forgetfulness. End quote. 
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: The fuqaha’ (may Allah have mercy on him) said: If he starts to say the takbeer before he bends down, or he completes it after reaching the bowing posture, then that is not valid, because they said that this takbeer is for movement and its place is between the two postures. If it is included in the first posture it is not valid and if he includes it in the second posture it is not valid, because that is a place where this dhikr is not prescribed. It is not prescribed to say takbeer whilst standing or whilst bowing, rather the takbeer comes in between standing and bowing. 
Undoubtedly this view is valid to some extent, because the takbeer is the sign of movement, so it should be done whilst moving. 
But the view that his prayer is invalidated if he completes it after he reaches the bowing position or he starts it before he starts to bend down causes hardship for people, because if you think about how people are nowadays, many people do not know this, and some of them say takbeer before they start to bend down, and some of them reach the bowing position before they finish saying it. 
It is strange that some ignorant imams have come up with a mistaken ijtihad and say “I will not say takbeer until I reach the bowing position, because if I say takbeer before I reach the bowing position, the people praying behind me will bow before I do, and they will bend down before I reach the bowing position, and perhaps they will reach it before I do.” This is a strange kind of ijtihad, whereby you would invalidate your own worship, according to the view of some scholars, in order to ensure the validity of the worship of someone else who is not enjoined to do things before you, rather he is enjoined to follow you. 
Hence we say: this ijtihad is inappropriate, and we call the one who comes up with this kind of ijtihad ignorant … because he is ignorant and he does not know that he is ignorant. 
If, let’s say, you say takbeer when you bend down, and you want to finish it before you reach the bowing position, but you reach the bowing position before you finish it, there is nothing wrong with that. 
The correct view is that if he starts the takbeer before bending down to bow, and finishes it after that, there is nothing wrong with that. If he starts it when he is bending down and ends it after he reaches the bowing position, there is nothing wrong with that. But it is better for it to be done between the two postures as much as possible. The same applies during the saying of “Sami’a Allahu liman hamidah” and all the takbeeraat of movement. But if he does not start until after he reaches the position that comes next,  then this is not valid.  End quote from al-Sharh al-Mumti’. 
And Allah knows best.