Hadith.1216 - Mu'awiyah ibn Sharih reported from Imam Jafar ibn Muhammad Al-Sadiq عليه السلام that He said:
"If a person comes quickly while the Imam is in ruku' (bowing), one takbir (saying 'Allahu Akbar') suffices for him to enter the prayer and perform the ruku'."
If someone joins the Imam while he is in Sujood (prostration), he should say the takbir and join in Sujood with him, but it will not be counted (as a rak'ah).
If a person joins the Imam in the last rak'ah, he attains the merit of the congregation.
If he catches the Imam after he has raised his head from the final prostration and is in the tashahhud (final testimony), he has caught the congregation, and there is no need for adhan or iqamah.
If he joins after the Imam has concluded with the taslim (salutation of peace), he must perform the adhan and iqamah.
It is not permissible to have two congregations for the same prayer.