ANSWER:

This is not permissible at all! 

You must pray fajr on time as this is something mandatory while praying tahajjud is sunnah.

I get up at 3am for tahajud, but the azan for fajr is given at 545am. So sometimes i lie down for a while to rest but fall asleep and miss my fajr prayer. So i offer it after i wake up in the morning at about 8am or 9 am. Is it fine? Or should i miss tahajud?cuz somebody said preferable time of tahajud is 3am