Whoever prayed alone then another Person joined Him, is His Prayer correct?

Question :

If I entered the mosque after the congregational prayer had finished and I began to pray, making the opening Takbir, then a man arrived after me and joined me in my prayer, when I had not intended this. Is his prayer correct or not?

Question :

The correct opinion is that it is lawful for you to make the intention to be the Imam when one or more persons join you in prayer, because the congregation is required and there is great virtue in it.

Some scholars held that this is only permissible in the non- obligatory prayers, but the correct view is that it is permissible in obligatory and non-obligatory prayers, because the basic principle is that that they are essentially the same in rulings, except where some evidence proves otherwise; and it has been authentically reported from him that he prayed alone at night in the house of Maimunah, the maternal aunt of Ibn 'Abbas may Allah be pleased with all of them and Ibn 'Abbas, may Allah be pleased with him, got up and made Wudhu' and stood on his right side, but the Prophet moved him until he was on his right side and led him in prayer..."!!

Muslim narrated in his Sahih from the Prophet that he was praying alone and Jabir and Jabbar (may Allah be pleased with them both) came and prayed on his right and left sides, but he placed them both behind him and led them in prayer." These two Hadiths prove what we have mentioned, just as they prove that one person should stand on the Imam's right, but that two or more stand behind him.

Source:
Ibn Baz
Fatawa Islamiyah, Vol. 2 Pages 177-178