Al salam alykom..
if i pray (ma’mom) and the immam finished the salaht.. but I didn’t so I stood to complete
my salaht .. then a person came to pray with me as a ma’mom ? Is my immamah correct?
wa jazak allah kyran.

Praise be to Allah.

If a person joins you wanting to pray with you, and you make the
intention of leading him in prayer, this is OK.

The author of the book Nihaayat al-Zayn fi Irshaad
al-Mubtadi’een
(p. 127) said: “If the imaam says salaam then one latecomer
decides to follow another latecomer in prayer, this is OK.”

And Allah knows best.