Is it recommended for a person outside the mosque to enter for prayer when the congregational prayer has already commenced?
Chapter on the Times When Prayer is Prohibited
Al-Mughni
Book of Prayer
Primary text
If the call to prayer has been made and the congregational prayer has commenced while a person is leaving the mosque, entering the prayer with the congregation is recommended only if the time is not one of the disliked times for voluntary prayer. If the time is permissible, it is recommended for him to enter the prayer with them. There is no issue if he enters and prays with them, supported by the narration concerning Abu Musa.
Supporting text
It is not recommended for him to enter and join the prayer if he is outside when it begins, as narrated by Mujahid who observed Ibn Umar stopping outside the mosque until the people finished praying, stating he had already prayed in his house. This narration is recorded by Imam Ahmad in the Musnad.