Sahih al-Bukhari Book 10, Hadith 24
The prophet said, "There is a prayer between the two Adhans (Adhan and Iqama), there is a prayer
between the two Adhans." And then while saying it the third time he added, "For the one who wants
to (pray).
Allah's Messenger (ﷺ) used to pray two light rak`at before the morning (compulsory) prayer after the day dawned and the Mu'adh-dhin had finished his Adhan. He then would lie on his right side till the Mu'adh-dhin came to pronounce the Iqama.
I came to the Prophet (ﷺ) with some men from my tribe and stayed with him for twenty nights. He was kind and merciful to us. When he realized our longing for our families, he said to us, "Go back and stay with your families and teach them the religion, and offer the prayer and one of you should pronounce the Adhan for the prayer when its time is due and the oldest one amongst you should lead the prayer."