What is the ruling regarding someone who joined a prayer in progress and caught one rak'ah with the Imam, then stood for the second rak'ah and did not perform the tashahhud until the third and fourth rak'ahs?

The issue is based on the scholarly disagreement regarding what a latecomer (masbuq) catches up on: is it the beginning of his prayer or its end? The preponderant opinion for us is that what the latecomer catches up on is the beginning of his prayer.

Scholars have differed on the place where the latecomer sits for the tashahhud, and the matter is broad in this regard. Whether he sits in the first rak'ah he has to make up (al-maqdiyyat) or in the second, all is permissible, as Ibn Qudamah preferred. Al-Athram narrated with his chain of transmission from Ibrahim, who said: "Jundub and Masruq came to the mosque, and two rak'ahs of the Maghrib prayer had already been prayed. They entered the row, and Jundub recited in the rak'ah he caught up with the Imam, while Masruq did not recite. When the Imam gave the salutation, they both stood up for the second rak'ah. Jundub recited, and Masruq recited. Masruq sat in the second rak'ah, while Jundub stood. Masruq recited in the third rak'ah, and Jundub did not recite. When they finished the prayer, they went to Abdullah and asked him about it, narrating the story to him. Abdullah said: 'It is as Masruq did that one should do.' Abdullah also said: 'If you catch up with one rak'ah of Maghrib, then sit in all of them.' And whatever is done of that is permissible, Allah willing. For that reason, Abdullah did not object to Jundub's action, nor did he order him to repeat his prayer."

It is more preferable to perform the tashahhud in the first of the rak'ahs to be made up (al-maqdiyyat) because it is stronger in evidence and sounder in reasoning, and due to the statement of Ibn Mas'ud: "It is as Masruq did that one should do."