No need to repeat the Fajr Sunnah if the adhan was after the dawn had appeared

Q: I entered the mosque for the Fajr prayer and prayed two rak'ahs. When I stood up for the second rak'ah, the mu'adhdhin stood up to call the adhan for the prayer. I had intended in that prayer that it was the Fajr Sunnah, as I had left my home while the adhan was being called in some of the mosques. When I finished my prayer, I sat down to read the Qur'an. A person next to me said to me: "Stand up and pray the Fajr Sunnah." I said to him: "I have already prayed it." He said: "It is not permissible unless you pray it again, because the mu'adhdhin called the adhan while you were praying." I ask you to inform me about this?

A: If the mu'adhdhin who called the adhan while you were praying the Fajr Sunnah delayed the adhan and your performance of it coincided with after the dawn had appeared, then you have performed the Sunnah, and that is sufficient, and there is no need to repeat it. However, if you are in doubt about that and do not know whether the mu'adhdhin who called the adhan while you were in prayer called it after the dawn or at the appearance of the dawn? Then the most cautious and best course for you is to repeat the two rak'ahs, so that you have performed them after the dawn had appeared with certainty.