Should one prostrate if he has not completed Witr prayer, or if he was supplicating, and the Fajr adhan was called before he could complete Witr?

The time for Witr prayer extends from after the 'Isha prayer until the appearance of dawn. If the muezzin calls the adhan for Fajr while the worshiper is in the middle of Witr prayer, he should complete his prayer, and there is no blame upon him, as mentioned by Ibn Baz and Ibn Uthaymeen.