Ibn Khuzaymah

He is not considered one who has said the takbir until he has finished the takbir and completed the letter "ra" which is the last letter of the takbir. The difference between his saying: "When he says the takbir, then say the takbir," and his saying: "When he bows, then bow, and when he prostrates, then prostrate," is that the name "one who says the takbir" does not apply to the imam until he completes the takbir, whereas the name "one who bows" may apply to him when he is settled in bowing, and likewise the name "one who prostrates" applies to him when he is settled in sitting.

Sayyiduna Abu Sa‘id Khudri (may Allah be pleased with him) narrates that the Messenger of Allah (peace and blessings be upon him) said: "When the Imam says « اللهُ أَكْبَرُ », then you say « اللهُ أَكْبَرُ ». When he says « سَمِعَ اللهُ لِمَنْ حَمِدَهُ », then you say « رَبَّنَا وَلَكَ الحَمْد »."