The ruling on the prayer of one who catches the imam in the second rak'ah and is uncertain about the rak'ah

Question:
A man caught up with the congregation in the second rak'ah of the Fajr prayer, so he said the takbir for the prayer. Then the imam bowed, and the man recited the opening supplication (du'a al-istiftah). Then he said the takbir for bowing, but he did not complete the supplication for bowing. Then the imam raised his head, and the man became uncertain whether that rak'ah counted for him or not. When the imam finished the prayer, he stood up and prayed two rak'ahs. Is what he did valid?

Answer:
He caught up with one rak'ah, and he caught up with the imam in the rak'ah or before the bowing, and he bowed with him. If he catches up with the bowing and bows with him, that rak'ah is valid for him. If the imam finishes the prayer, he is only required to have one rak'ah. And if he left saying "Subhan Rabbi al-Azim" (Glory be to my Lord, the Exalted), which is obligatory, and he did not say "Subhan Rabbi al-Azim" while prostrating on the ground, yes. He has an addition, but since it is permissible, it is not valid for him to repeat the prayer. No.