Is a Muslim's prayer between the two adhans for the Fajr prayer valid?

If the question is about the Nafilah (supererogatory prayer) between the Adhan of Fajr and its Iqamah, scholars have differed on performing more than the two rak'ahs of Ar-Raghibah (the confirmed sunnah of Fajr). However, if the question is about the Nafilah between the first Adhan (before the time of Fajr enters) and the second Adhan (when the time enters), then prayer at this time is unequivocally permissible and is considered part of Qiyam al-Layl (night vigil prayer), and no scholar forbids it. As for the obligatory prayer (Fard), it is not valid until after its time has entered.