What is the Sunnah regarding raising the hands from the middle tashahhud when standing for the third rak'ah for one who is catching up to the prayer (masbuq), and is it only the masbuq who raises them, and what if the Imam does not raise his hands?

Raising the hands when standing up from the first tashahhud is a sound and established Sunnah from the Prophet, peace and blessings be upon him. For someone who joins the Imam in the second rak'ah, it is prescribed for him to raise his hands when standing up from the first tashahhud, whether his Imam raises them or not. Similarly, when standing up for the third rak'ah, it is prescribed to raise the hands.