[Lengthening bowing (rukūʿ) or recitation to allow a latecomer to catch the prayer]

Answer: This is permissible according to the school. As for the statement in al-Azhār, “The imām should not add beyond what is customary in waiting,” the marginal note comments: “Meaning: it is Êrecommended that he not add.”
They generalize this ruling to recitation and bowing, saying that adding beyond the customary amount is Êdisliked, but does not Êinvalidate the prayer; they explain the lack of invalidation by saying that even if it is a lengthy addition, it is still in its proper place.
I say: What is preferable is that waiting for the latecomer so he may attain the congregation should not be deemed disliked; rather, it is recommended and legislated. Waiting occurs in the prayer of fear (ṣalāt al-khawf), which Allah commanded in His saying: “And let another group come forward that has not prayed, and let them pray with you.” [An-Nisāʾ:102] This verse entails a command to the Prophet—may Allah bless him and his family and grant them peace—to lengthen the second rakʿah so that the second group could catch the prayer with the Prophet may Allah bless him and his family and grant them peace; and it is authentically related that he (may Allah bless him and his family and grant them peace) did just that in ṣalāt al-khawf. There is no doubt that his lengthening in that prayer was so the other group might attain the virtue of congregation.
They have also adduced—supporting this—what is related in ash-Shifāʾ and elsewhere: that the Prophet—may Allah bless him and his family and grant them peace—would lengthen the recitation when he sensed someone entering to join the prayer; he would stand in the first rakʿah of Ẓuhr so long that the placing of a foot could not be heard.
What we have mentioned is further attested by His saying: “Help one another in righteousness and piety, and do not help one another in sin and transgression.” [Al-Māʾidah:2]
If it is said: The imām is commanded to lighten the prayer, as in the ḥadīth concerning Muʿādh—
We reply: In other than what we have stated—this reconciles the evidences; and reconciling them is better than acting by some and abandoning others.
Indeed, what we have stated—that lengthening is recommended—is the view of Imām al-Muʾayyad bi-llāh and Imām al-Manṣūr bi-llāh—peace be upon them—as in Sharḥ al-Azhār.
It also says therein: al-Manṣūr bi-llāh held that his tasbīḥ may reach twenty.
Source : Min Thimār al-ʿIlm wa al-Ḥikmah vol.1