Answered by Shaykh Hamza Karamali, SunniPath Academy Teacher
May a follower in the group prayer continue saying the blessings on the Prophet, sallallahu alayhi wa sallam, in the first tashahhud of a three or four raka’a prayer if the Imam prolongs his tashahhud longer than the followers?
In the Name of Allah, Most Merciful and Compassionate
Shaykh ‘Abd Allah al-Jurdani, a student of Shaykh al-Bajuri (Allah have mercy on them both) said in his book, Fath al-‘Allam bi Sharh Murshid al-Anam:
“If the follower finishes his first tashahhud before the imam, he should either (1) remain silent or (2) perform some remembrance of Allah (dhikr) or supplication (du‘a). The latter is superior to remaining silent; rather, it is what is recommended.
All of this applies if he is not a latecomer (idha kana muwafiqan). If he is latecomer (masbuq), such as if he catches two rak‘as of a four rak‘a prayer, then according to Ramli, he should finish the final tashahhud and whatever follows it (including the blessings on the family of the Prophet), whereas according to Ibn Hajar, he should not complete it, but rather (h: just recite the tashahhud) and then perform some remembrance of Allah or supplication.
… If the tashahhud is the final tashahhud for the imam and not the first tashahhud for the (h: latecomer) follower, there is agreement that he should either complete the tashahhud (h: and whatever follows it) out of following the imam or busy himself with some remembrance of Allah or supplication.
If the tashahhud is not the first tashahhud for the (h: latecomer) follower and is the first tashahhud for the imam, then there is agreement that he should not complete what follows the tashahhud but rather either (1) remain silent or (2) busy himself with remembrance of Allah or supplication. This (h: the latter) is superior, just like what has preceded above.” (Fath al-‘Allam, 2.247,248)
And Allah knows best.
Hamza.