Is the prayer considered to have been caught if the Imam was caught in the bowing position (ruku'), while forgetting the transitional takbir after the opening takbir, and does the Imam bear the congregant's oversight regarding the transitional takbir?

A worshiper catches the prayer by catching the Imam before the Taslim (salutation), and catches the Rak'ah (unit of prayer) if he catches the bowing without doubt. The criterion is his bending and catching the bowing before the Imam begins to rise from it. The Takbirat al-Intiqal (transitioning Takbir) is Sunnah (recommended) and not obligatory if the worshiper catches the Imam while he is bowing. The Imam bears the worshiper's forgetfulness.