If the imam says the salaam and the person praying behind him has not finished the tashahhud, what should he do?
Question

                If I am reciting the tashahhud and I have not completed it, and the imam says the salaam, should I stop saying it?.
Praise be to Allah.
    The final tashahhud is one of the pillars or essential parts 
    of the prayer, and it must be completed in full, because Ibn Mas’ood (may 
    Allaah be pleased with him) said: Before the tashahhud was enjoined upon us, 
    we used to say, ‘Peace be upon Allaah before His creation, peace be upon 
    Jibra’eel and Mikaa’eel.’ Then the Messenger of Allaah  (peace and 
    blessings of Allaah be upon him) taught us the tashahhud. Narrated by 
    al-Nasaa’i (1277), al-Daaraqutni and al-Bayhaqi; classed as saheeh by 
    al-Haafiz ibn Hajar in al-Fath (2/312) and by al-Albaani in Irwa’ 
    al-Ghaleel (319). 

    The phrase “before the tashahhud was enjoined upon us” 
    clearly indicates that the tashahhud is obligatory. 

    See: al-Sharh al-Mumti’ (3/422). 

    Hence if the imam says the salaam before the person praying 
    behind him has completed it, then he should not follow him, rather he should 
    complete his tashahhud first. 

    It says in Kashshaaf al-Qinaa’ (1/565): 

    If the Imam finishes his recitation before the one who is 
    praying behind him and bows, then the one who is praying behind him should 
    follow him, and stop his own recitation, because in his case reciting is 
    mustahabb, but following the imam is obligatory, and there is no conflict 
    between what is obligatory and what is mustahabb, unlike the tashahhud 
    where, if the imam finishes before the one who is praying behind him, the 
    latter should not follow him, rather he should complete the tashahhud when 
    the imam says the salaam, then say salaam, because of the general meaning of 
    the command to recite the tashahhud. 

    End quote. 

    With regard to the sending of blessings upon the Prophet  
    (peace and blessings of Allaah be upon him), in the answer to question no. 
    39676 we have stated that there is a difference of opinion among the 
    scholars concerning that. Some of them say that it is a pillar or essential 
    part of the prayer, and others say that it is Sunnah and mustahabb. 

    The Prophet  (peace and blessings of Allaah be upon him) 
    enjoined the one who has completed the final tashahhud to seek refuge with 
    Allaah from four things. He said: “When one of you finishes reciting the 
    final tashahhud, let him seek refuge with Allaah from four things: from the 
    punishment of Hell, from the punishment of the grave, from the trials of 
    life and death, and from the evil of the Dajjaal.” Narrated by Muslim 
    (588). 

    Some of the scholars are of the view that reciting this 
    du’aa’ is obligatory.  

    Based on this, then in order to be on the safe side, the 
    person who is praying behind an imam should not say the salaam until he has 
    completed the tashahhud and sent blessings upon the Prophet  (peace and 
    blessings of Allaah be upon him), and sought refuge with Allaah from these 
    four things.  

    Shaykh Ibn Baaz (may Allaah have mercy on him) was asked: 
    During the prayer, the imam said the salaam and I had only completed a small 
    part of al-tahiyyaat. Should I repeat my prayer? 

    He replied: You have to complete the tashahhud even if it 
    means that you are a little behind your imam, because the final tashahhud is 
    a pillar or essential part of the prayer according to the more correct of 
    the two scholarly opinions, and it includes sending blessings upon the 
    Prophet  (peace and blessings of Allaah be upon him).  

    So what you have to do is complete it, even if that is after 
    the imam says the salaam. It also includes seeking refuge with Allaah from 
    the punishment of Hell, the torment of the grave, the trials of life and 
    death and the trial of the Dajjaal, because the Prophet  (peace and 
    blessings of Allaah be upon him) enjoined seeking refuge from these four 
    things in the final tashahhud, and because some of the scholars said that 
    this is obligatory. And Allaah knows best. End quote. 

    Majmoo’ Fataawa Ibn Baaz 
    (11/248).