You must exert more effort by sincerely asking Allah to help you be punctuate to observe Fajr prayer. Tahajjud is an optional prayer which cannot substitute Fajr which is an obligatory prayer. It must be observed on time which is between the appearance of the true dawn until the sun rises.

 

If a person misses Fajr due to being asleep, he must observe it immediately when he wakes up. Qatada reported on the authority of Anas b. Malik that the Messenger of Allah (peace be upon him) said: When any one of you misses a prayer due to sleep or he forgets to perform it, he should observe it when he remembers it, for Allah has said:” Observe prayer for remembrance of Me.” (Muslim)

 

Therefore, if you wake up after sunrise, you must observe the prayer of Fajr. You cannot leave it or substitute it with any other prayer either obligatory or supererogatory.

Allah knows best.