Ruling on joining the prayer behind a latecomer who is completing his prayer

Question:
A man stood up to complete his prayer, then another man entered the mosque and led him in prayer. What is the ruling on this action?

Answer:
There is no blame in that, and it is better if each person makes up his own missed portion; because when the Prophet (peace and blessings be upon him) missed a unit of prayer with al-Mughirah, each of them made up what remained alone, as in Sahih Muslim from al-Mughirah ibn Shu'bah regarding the Battle of Tabuk. He said: The Prophet (peace and blessings be upon him) went to relieve himself during the Fajr prayer. When he returned, he performed ablution, and he was wearing two leather socks. When I tried to remove them so he could wash his feet, he said: So he wiped over them. He said: Then we went to the army's location and found that they had appointed 'Abd al-Rahman ibn 'Awf to lead them in prayer. The Prophet (peace and blessings be upon him) arrived, and 'Abd al-Rahman had already prayed one unit. When 'Abd al-Rahman saw him, he wanted to step back, but the Prophet (peace and blessings be upon him) gestured to him to continue and complete his prayer. Then the Prophet (peace and blessings be upon him) lined up with al-Mughirah among the people, and they had missed one unit. When 'Abd al-Rahman concluded the prayer, the Prophet (peace and blessings be upon him) and al-Mughirah each stood up separately to make up the unit they had missed. This indicates several benefits, among which is: if the imam is delayed beyond his usual time, it is prescribed for the followers to appoint someone to lead them in prayer, and they are not required to wait for him, and it is not permissible for him to object to them.
And among them is: if a person misses something of his prayer, he makes up what he missed after the closing salam.