How should a latecomer to the prayer deal with the middle and final Tashahhud in the Maghrib and Isha prayers? Should he recite them with the Imam or what should he do?

What a latecomer catches up with the Imam is considered the beginning of their prayer, according to the more preponderant opinion. So, if you miss one rak'ah of Maghrib, you perform one rak'ah with only Al-Fatihah silently, then you recite the tashahhud and say the taslim. If you miss two rak'ahs of Maghrib, you perform one rak'ah with Al-Fatihah and a surah aloud and then recite the tashahhud, then perform one rak'ah with only Al-Fatihah silently, then recite the tashahhud and say the taslim.

If you miss one rak'ah of Isha, you perform it with only Al-Fatihah, then recite the tashahhud and say the taslim. If you catch only two rak'ahs of Isha, you perform them with only Al-Fatihah, then recite the tashahhud and say the taslim. It is obligatory to follow the Imam in both tashahhuds, and it is recommended to recite the prescribed remembrances therein.