What is the ruling regarding the prayer of a worshipper who prostrates before the Imam says "Allahu Akbar" while on his way to prostration, and is his prayer valid?

It is Sunnah for the Imam to pronounce the takbir aloud when beginning the transition, and similarly for the rest of the dhikr of transition. Intentionally delaying the takbir until reaching prostration invalidates the prayer according to the correct view of the Hanbali school, who consider the takbirat al-intiqal (transition takbirs) obligatory. As for the majority of scholars, they consider them Sunnah, so the prayer is not invalidated by omitting them or performing them out of place.

The prayer of one who precedes the Imam is valid, but he is sinful.