Fiqh-us-Sunnah Volume 2, Supererogatory Prayer, Fiqh 2.052.

Section : The imam may prolong the first rak’ah to allow others to join.

It is permitted for the imam to prolong the first rak’ah while waiting for others to join the congregation. In the same way, it is preferred for him to wait for people who are coming during the bowings and during the final sitting.

Abu Qatadah reports that the Prophet sallallahu alehi wasallam would prolong the first rak’ah and the people suspected that he did it to allow the late-comers to join the first rak’ah. Abu Sa’id says: “If the (congregational) salah was begun, one could go to al-Baqi’, relieve himself, make wudu’, and return and find the Prophet still in the first rak’ah for he would prolong it (first rak’ah).” This is related by Ahmad, Muslim, Ibn Majah, and an-Nasa’i.