Wa `alaykum As-Salamu wa Rahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
Focusing more on your question, Sheikh Ahmad Kutty, a senior lecturer and Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states:
Prayer has a certain time in which a Muslim should offer it. Allah says, “Worship at fixed hours hath been enjoined on the believers.” (An-Nisaa’ 4:103)
Also, the Prophet (peace and blessings be upon him) warned against ignoring offering Prayers in their due times.
Fajr time starts with the first appearance of dawn. The preferred time to pray Fajr is soon after without much delay while it is still dark. This, according to the majority of imams and scholars, had been the consistent practice of the Prophet (peace and blessings be upon him), as we can readily infer from the authentic traditions.
If, however, you were to wake up late, then you should pray before sunrise. It does not matter whether it is clear outside or not. The Prophet (peace and blessings be upon him) said, “If anyone oversleeps and misses a Prayer, he should do it as soon as he wakes up or remembers it.”
As far as the permissible time limit for Fajr, it extends from first break of dawn until sunrise. If, however, you were to wake up at the time of sunrise, you should wait for half an hour until the sun has risen well. This is because of the clear prohibition in the hadith about praying at the time of sunrise.
Almighty Allah knows best.
Excerpted, with slight modifications, from: www.muslims.ca