Does one achieve the virtue of Witr prayer if they pray Witr three rak'ahs with one tashahhud, and they caught the bowing of the first rak'ah, then the time for Fajr entered while they had not caught the second or third rak'ah?

The time for Witr ends with the break of dawn (Fajr). If a worshipper catches the bowing (rukūʿ) of the first rakʿah of Witr before dawn, he has missed Witr in its prescribed time according to the majority of scholars, who hold that whoever catches less than one rakʿah has not caught the prayer in its time. They cite as evidence the hadith (definition): "Whoever catches one rakʿah of the prayer has caught the prayer." There is also a view among some scholars that whoever catches less than a full rakʿah before the time expires has caught that prayer within its time.