Answer
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
If a person comes late to the mosque and the people have already prayed, and he finds someone who joined the prayer late still praying, it is prescribed for him to pray with him and to stand to the right of the one who had joined the prayer late, seeking the reward of praying in congregation.
Answering your question, the late Saudi scholar, Sheikh Ibn Baz (may Allah have mercy on him) stated:
If a person comes late to the mosque and the people have already prayed, and he finds someone who joined the prayer late still praying, it is prescribed for him to pray with him and to stand to the right of the one who had joined the prayer late, seeking the reward of praying in congregation.
The one who had joined the prayer late should then intend to lead the other man. There is nothing wrong with that according to the more correct of the two scholarly opinions.
Similarly, if he finds a man praying alone after the imam has said the salam, it is prescribed for him to pray with him and to stand on his right, seeking the reward of praying in congregation.
When the one who had joined the prayer late or the one who was praying alone says the salam, then the one who came in last should stand up and complete his prayer, because of the general meaning of the evidence which speaks of the virtue of praying in congregation. It was also proven that when the Prophet (peace be upon him) saw a man who had entered the mosque after the prayer was over, he said, “If anyone wants to do this man a favour, let him pray with him.” (Abu Dawud)
Almighty Allah knows best.
Source: https://islamqa.info/en/21765