What is the ruling on one who prays Tarawih in the mosque behind the Imam, and remains seated in the row during the first rak'ah, and does not say "Allahu Akbar" with the Imam until the Imam bows, and then completes his prayer? And is his prayer valid?

What this man does by sitting in the row before the prayer and then joining it at the bowing (ruku') involves several violations: he breaks the row, misses the virtue of the opening takbir (takbirat al-ihram) and listening to the Imam's recitation in prayer, and it may suggest his annoyance with the prayer, which could deprive him of the reward of "whoever stands (in prayer during) Ramadan with faith and anticipation of reward." He also deliberately enters into a scholarly dispute regarding the issue of catching the rak'ah by bowing. He should be advised to abandon this action. If he is tired from prolonged standing, he may sit and pray while sitting, and he will receive half the reward of one who stands if he is able (to stand), and a full reward if he is unable.