The ruling on one who catches up with the congregation but has not yet prayed the previous obligatory prayer

He says: I slept before the midday prayer, and when I woke up, I found people in the mosque praying the midday prayer. I thought they were praying the afternoon prayer, so I joined them with the intention of praying the afternoon prayer. Do I have to pray the midday prayer after the prayer is finished, or not? And when should I pray it? May Allah grant you success.
Answer: In the name of Allah, the Most Gracious, the Most Merciful. Praise be to Allah, and blessings and peace be upon the Messenger of Allah, and upon his family and his Companions, and upon those who follow his guidance.
As for the answer to this questioner, there is a distinction: If, when he prayed the afternoon prayer with them, he thought he had already prayed the midday prayer, and in his belief he had prayed the midday prayer, and he thought they were praying the afternoon prayer because in his belief he had already prayed the midday prayer, then his afternoon prayer is sufficient for him, and he must pray the midday prayer afterwards. This is because he prayed the afternoon prayer while thinking he had already prayed the midday prayer, so his prayer is valid.
However, if he intentionally prayed the afternoon prayer while knowing that he owed the midday prayer, then it does not suffice for him. He must repeat the afternoon prayer after he prays the midday prayer. He prays the midday prayer first, then he prays the afternoon prayer. This is because Allah has arranged this after that, so it is obligatory to perform it as Allah has prescribed it. He prays the midday prayer first, then he prays the afternoon prayer. But if a person prays the afternoon prayer while forgetting, thinking he does not owe the midday prayer, and then it becomes clear that he owed the midday prayer after he had prayed the afternoon prayer, then his afternoon prayer is sufficient for him. Yes.