Is it permissible to perform تحية المسجد (two rak'ahs upon entering the mosque) before the Fajr adhan, and then pray the two rak'ahs of Fajr (Sunnah) after the adhan?

Tahiyat al-Masjid (greeting of the mosque) is required as soon as one enters the mosque. If you enter it before the Fajr (dawn) adhan (call to prayer), do not sit until you have prayed two rak'ahs (units of prayer), because the Prophet, peace and blessings be upon him, said: "When one of you enters the mosque, let him not sit until he has prayed two rak'ahs." After the Fajr adhan, you pray the two rak'ahs of the Sunnah of Fajr, and it is not valid except after the true dawn appears.