Assalamu alaikum, does it have any effect on the validity of the congregational prayer of the latecomer if the imaam is in rukoo and and then the latecomer makes only one takbeer (takbeeratul ihram) and then he comes down for rukoo but he has not finished the pronunciation of takbeeratul ihram (he says takbeeratul ihram and while he has not finished it he moves to bow for rukoo, so that he says a part of takbeeratul ihram while he starts to bow). I hope you could understand my description. Jazakum Allahu khayran.

All perfect praise be to Allaah, The Lord of the Worlds.  I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.

For the Takbeeratul-Ihraam [the Takbeer for starting the prayer] to be sufficient and valid, it is a condition that the praying person says it while standing (in the standing position). In case he says it while he is not standing or that he only says a part of it while standing, then his prayer is not valid as an obligatory prayer.

Al-Buhooti said in his book entitled “Ar-Rawdh Al-Murbi’”: “In case the praying person says the Takbeeratul-Ihraam while he is not in the standing position, or that he started saying it or finished saying it while he is not in the standing position, then this prayer is valid as a supererogatory prayer if he has enough time to complete the supererogatory prayer and to commence the obligatory prayer before its prescribed time expires.” For more benefit, please refer to Fatwa 85247.

In the light of the above, the answer to your question has become clear to you; so if the person who is preceded in prayer joins the prayer while the Imaam is in Rukoo’ (in the bowing position), he is obliged to say the entire Takbeer while standing; otherwise his prayer is not valid as an obligatory prayer.

Besides, you should know that the limit of the Qiyaam (standing) position is that the praying person does not reach the level of Rukoo’, this is when his hands cannot touch his knees, so if he completes the Takbeer while going down for Rukoo’ but he is in a position that could be called as standing in a way that his hands cannot reach his knees, then he is considered as saying Takbeer while in the standing position and his prayer is valid as an obligatory prayer.

An-Nawawi said in his book entitled “Al-Majmoo’”: “The limit that distinguishes between the Rukoo’ position and the Qiyaam position is when one's palms reach his knees when he extend his hands, so this is the extent of Rukoo’ position and before this, it is considered as the Qiyaam position.”

On the other hand, according to the Hanbali School of jurisprudence, it is sufficient for him (the latecomer) to only say the Takbeeratul-Ihraam without saying the Takbeer for Rukoo’, so he may go down for Rukoo’ without (another) Takbeer and his prayer is valid. However, it is more appropriate for him to say the Takbeer when going down for Rukoo’ as well. For more benefit, please refer to Fatwa 88883.

Allaah Knows best.