What is the ruling on the prayer of an imam who moves his index finger when reciting Al-Fatihah and verses during prayer, is his prayer permissible, and what is the ruling on the prayer of those praying behind him?

The movement of a worshiper's finger while reciting the Quran is not legislated, but it does not invalidate the prayer. Minor, successive movements, such as moving fingers on prayer beads, scratching, or similar actions, do not invalidate the prayer according to the soundest opinion, as this does not detract from the state of humility and reverence. Therefore, the prayer of one who moves his finger is valid, according to the correct view, and so is the prayer of the congregants behind him.