The Ruling on Delaying the Fajr Prayer Past Its Time
Quick answer: There's a key difference between praying Fajr slightly later within its window and missing it entirely after sunrise.
The Fajr prayer window runs from true dawn until just before sunrise. Praying it later within that window — rather than right at its start — is permissible, though praying it early carries greater reward.
But once the sun rises, the window has closed and the prayer is now considered missed (qada), to be made up immediately upon waking or remembering, based on the Prophet's ﷺ statement that whoever sleeps through or forgets a prayer should pray it as soon as they remember — that is its only expiation.
Someone who unintentionally oversleeps or forgets Fajr bears no sin and simply prays it upon waking, even after sunrise. Someone who deliberately delays it without excuse until it's missed, however, is considered by the majority of scholars to have committed a serious wrong, requiring both repentance and making up the prayer.
To avoid missing Fajr, many scholars recommend setting multiple alarms, sleeping early, and checking your city's exact Fajr time daily, since it shifts slightly every day.