Appointing someone else to take over as imam during the prayer
Question

                Is it permissible to change imams during the prayer, starting from the second rak’ah, because the imam cannot complete the prayer or the recitation of Qur’aan because he is crying so much and he is afraid that he may make the prayer too long for those who are praying behind him, and they are on a journey or are in a hurry, so he appoints someone from the congregation to take over leading the prayer during the prayer, and they trade places and complete the prayer from that point? If what they did is not permissible what should the imam do? What should those who were praying behind him do? What should the replacement imam do?.
Praise be to Allah.
    Firstly: 

    If a reason arises which prevents the imam from completing 
    the prayer or from continuing as the imam, he may appoint someone to take 
    over for him and complete the prayer with the congregation. This is the view 
    of the majority of te scholars. 

    Al-Nawawi (may Allaah have mercy on him) said in 
    al-Majmoo’ (4/142): 

    Ibn al-Mundhir narrated it from ‘Umar ibn al-Khattaab, ‘Ali, 
    ‘Ilqimah, ‘Ata’, al-Hasan al-Basri, al-Nakha’i, al-Thawri, Maalik, ashaab 
    al-ra’i and Ahmad, and he did not narrate from anyone that it is not 
    permitted to appoint someone else to take over. End quote. 

    They quoted as evidence the fact that when ‘Umar ibn 
    al-Khattaab (may Allaah be pleased with him) was stabbed as he was praying, 
    he took the hand of ‘Abd al-Rahmaan ibn ‘Awf and made him move forward, and 
    he led the people in the remainder of the prayer. Narrated by al-Bukhaari, 
    3700. 

    That was done in the presence of the Sahaabah and others, and 
    no one objected, so there was consensus. 

    See: al-Mawsoo’ah al-Fiqhiyyah (3/252) 

    Secondly: 

    If the imam becomes unable to complete the prayer or to do 
    any of the essential parts of the prayer, that is regarded as one of the 
    excuses which make it permissible for him to appoint someone else to 
    complete the congregational prayer. 

    Abu’l-Waleed al-Baaji said in al-Muntaqa Sharh al-Muwatta’ 
    (1/290): 

    With regard to the imam moving back because of an excuse, 
    there is no difference of opinion concerning the fact that this is 
    permissible. The excuses are of two types: 

    That includes something that makes the imam obliged to become 
    a member of the congregation, which is if he becomes unable to do any of the 
    obligatory parts of the prayer. In that case he should move back and make 
    another man move forward to complete the prayer and he should follow the new 
    imam. End quote. 

    Another example is if the imam is overcome with weeping and 
    he cannot complete the recitation of al-Faatihah, which is an essential part 
    of the prayer. In that case he should appoint a member of the congregation 
    to take over.  

    Ibn Qudaamah said in al-Mughni (1/944): 

    If he is unable to complete al-Faatihah, then he may appoint 
    someone to take over leading them in prayer, because he has become unable to 
    do it. And it is permissible to appoint someone else, such as if he breaks 
    his wudoo’ by accident or if he becomes unable during the prayer to do an 
    essential part of the prayer, then he may appoint someone to complete the 
    prayer. End quote.  

    But if the imam has finished reciting al-Faatihah, then he is 
    overcome with weeping whilst reciting Qur’aan after al-Faatihah, in that 
    case he may stop reciting and bow, and he does not have to do anything 
    else. 

    It was narrated that ‘Abd-Allaah ibn al-Saa’ib (may Allaah be 
    pleased with him) said: The Messenger of Allaah  (peace and blessings of 
    Allaah be upon him) led us in praying Fajr in Makkah, and he started to 
    recite Soorat al-Mu’minoon, until he came to the passage that mentions Moosa 
    and Haroon, when the Prophet  (peace and blessings of Allaah be upon 
    him) was overcome by coughing, so he bowed. Narrated by Muslim (455). 

    Al-Nawawi (may Allaah have mercy on him) said in Sharh 
    Muslim (4/177): 

    This hadeeth shows that it is permissible to stop reciting 
    and it is not makrooh to do so, if one stops for a reason. End quote. 

    It is not permissible for him to appoint someone else to take 
    over in that case, because he is able to complete the prayer with the 
    people, doing only the essential parts of the prayer. There is no need for 
    him to continue reciting with difficulty when weeping, because reciting 
    something else in addition to al-Faatihah is not obligatory. 

    In Mawaahib al-Jaleel (2/136) it is narrated that 
    al-Maaziri said: 

    He should not appoint someone to take over if he is prevented 
    from reciting part of the soorah. 

    In such cases it is recommended that he try to control 
    himself as much as he can, so that he will not cause any hardship to the 
    other worshippers if his weeping goes on for too long, as that will have 
    some negative effects.  

    Shaykh Ibn Baaz (may Allaah have mercy on him) was asked in
    Majmoo’ al-Fataawa (11/342): What is your opinion on the phenomenon 
    of weeping loudly? 

    He replied: 

    I have advised many of those who have gotten in touch with me 
    to avoid doing this and that it is not appropriate, because it annoys people 
    and causes hardship to them, and it distracts other worshippers and those 
    who are reading Qur’aan. What the believer should do is strive not to let 
    his voice be heard if he is weeping, and he should beware of showing off, 
    for the shaytaan may lead him to show off. He should not annoy anyone with 
    his voice, or disturb them. But it is known that some people do not do that 
    by choice, rather they get overwhelmed without meaning to. In this case it 
    is forgivable if he cannot help it. It is proven that when the Prophet  
    (peace and blessings of Allaah be upon him) recited Qur’aan, his chest would 
    heave like the boiling of a cauldron because of weeping. And it is narrated 
    that when Abu Bakr (may Allaah be pleased with him) read Qur’aan, he could 
    not make the people hear it because of weeping. And it is narrated that 
    ‘Umar’s sobs could be heard from behind the rows (of worshippers). But this 
    does not mean that the voice should be raised in weeping, rather it is 
    something that overwhelmed them because of their fear of Allaah. So if a 
    person is overcome with weeping and cannot help it, there is no sin on him 
    for that. End quote. 

    Thirdly: 

    From the above it is clear that if your imam had finished 
    reciting al-Faatihah, then he made a mistake when he appointed someone else 
    to take over, and he should not do that again. But the ruling on your prayer 
    and his is that the prayer is valid, in sha Allaah, and no one should be 
    told to repeat it, because you were all unaware of this ruling.  

    But if the imam is overcome with weeping whilst reciting 
    al-Faatihah, then what he did by appointing someone else to take over was 
    correct. 

    And Allaah knows best.