What is the ruling on the prayer of one who remained seated inadvertently after the Imam failed to say "Allahu Akbar" upon rising from prostration in the Fajr prayer, and how is the prayer to be rectified?

The prayer of those who were late in prostrating because they did not hear the Imam's takbir, and then prostrated after hearing it, is valid and there is nothing upon them. As for the others, if they made the taslim (definition) without prostrating, their prayer is invalid and must be repeated. If they prostrated before a long separation between the two prostrations, their prayer is valid. A long separation is defined as the time it takes to recite the prescribed supplication between the two prostrations, plus the time it takes to recite the shortest form of the tashahhud (definition).