Ruling on joining the prayer of one who is praying 'Asr with the intention of Zuhr

The following message was received by the program from the brother: Ya'qub 'Abd Allah Ahmad. He says: A Sudanese teacher residing in Yemen, our brother also has a number of questions. Among his questions is one that says: I disagreed with a colleague of mine regarding how to perform congregational prayer for two people, for example. In the time of the 'Asr prayer, if we know that one of them had forgotten and did not pray Zuhr, but he made it up in the time of 'Asr. The question is: Does he join his colleague in the congregational prayer for 'Asr, intending to pray Zuhr, and then after finishing, he prays 'Asr, or not?
Second: Which of the two leads the other if they intend to pray in congregation, and each intends a specific prayer, such as the first intending the Zuhr prayer and the second intending the 'Asr prayer, knowing that each of them fulfills the conditions for being an imam?
Answer: Yes, if it is like this, there is no harm in their praying in congregation. And it does not matter which one leads the other. If the one who wants to pray 'Asr leads, then the one who owes Zuhr prays behind him with the intention of Zuhr. When he finishes, he prays 'Asr afterwards according to the Shari'ah order. And if the one who owes Zuhr leads, because he is more knowledgeable in recitation or older or similar, then the one who owes 'Asr prays behind him in the time of 'Asr, praying it with the intention of 'Asr. This is what is obligatory. Yes.