Answered by Shaykh Faraz Rabbani
In the Salah, if the imam is in ruku and he realized that some person just joined the congregation, then is it ok for the imam to prolong the ruku little bit, so that the person can get that raka’.
Answer:
Walaikum assalam wa rahmatullah,
I pray that this finds you well, and in the best of health and spirits. May Allah grant you all good and success in this life and the next.
There is nothing wrong with doing so–as long as one does it for the sake of Allah; and to assist one’s fellow believer in the good; and doesn’t unduly prolong the ruku`. [Ibn Abidin, Radd al-Muhtar]
And Allah alone gives success.
Faraz Rabbani