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:
Joining the prayer behind a late person is a matter over which Muslim scholars have differed. Therefore, there is no need to criticize someone who follows the view that it is permissible for a late person to lead another person.
Answering your question, Sheikh Mustafa Umar, President of California Islamic University, states:
A person who joins the prayer late will continue to complete their prayer after the imam has finished.
While they are completing the remaining parts of the prayer that was missed, due to being late, the question arises about whether another late person, who missed the prayer completely, can make this person as their imam and pray behind them.
Imam Abu Hanifah said this is not permissible because the person began their prayer with the intention of following another imam. They cannot change their intention in the middle of prayer.
However, Imam Ash-Shafi`i disagreed and said that the intention to pray behind another imam is not a requirement.
I prefer the first opinion and do not think it should be done. However, note that this is a matter over which Muslim scholars have different views.
Therefore, there is no need to criticize someone who follows the other opinion.
Almighty Allah knows best.