Under which condition is a person permitted to perform the Sunnah of Fajr even after the congregational Fard has commenced?

Prohibited and Disliked Times of Prayer (الأوقات المكروهة)

• Only if they can perform them in the same row as the Imam.
• If they expect to catch any part of the Fard congregation, even the final Tashahhud, while performing the Sunnah outside the main rows.
• If the Imam is reciting a very short surah.
• There are no exceptions; one must join the Fard immediately.