If a person did not hear some of the phrases of the adhaan, it is not prescribed for him to say them
Question

                If the muezzin gives the adhaan and I only heard the end of the adhaan – for example – when he says “hayya ‘ala al-falaah” – for example - should I start saying the beginning of the adhaan quickly and then complete it with the muezzin, or is this not correct?.
Praise be to Allah.
    What seems to be the case to 
    us is that the one who has missed any part of the adhaan and did not hear it 
    should not say it, and that he should repeat after the muezzin from where he 
    hears it, and not that which he missed, because the apparent meaning of the 
    hadeeth is that repeating after the muezzin is connected to hearing him. 
    This view is the correct one, contrary to those who say that that is 
    permissible. 

    It was narrated from 
    ‘Abd-Allaah ibn ‘Amr ibn al-‘Aas that he heard the Prophet (blessings and 
    peace of Allaah be upon him) say: “When you hear the muezzin, say what he 
    says, then send blessings upon me, for whoever sends blessings upon me, 
    Allaah will send blessings upon him tenfold. Then ask Allaah to grant me 
    al-waseelah, for it is a station in Paradise which only one of the slaves of 
    Allaah will attain, and I hope that I will be the one. Whoever asks for 
    al-waseelah for me, intercession will be permissible for him.”

    Narrated by Muslim (384). 

    Al-Nawawi said:

    If a person sees the muezzin 
    and knows that he is giving the adhaan, but he cannot hear him because he is 
    far away or he is deaf, then it seems that it is not prescribed for him to 
    repeat after him, because repeating after him is connected to hearing, and 
    the hadeeth clearly states the stipulations, and by analogy with saying “yarhamuk 
    Allaah (may Allaah have mercy on you)” to one who sneezes, which is only 
    prescribed for the one who hears him say “al-hamdu Lillaah (praise be 
    to Allaah).” 

    Al-Majmoo’ 
    3/127 

    Shaykh Muhammad ibn Ibraaheem 
    Aal al-Shaykh (may Allaah have mercy on him) said: 

    If a person only hears part 
    of the adhaan, or he sees the muezzin but does not hear him, should he 
    repeat after him? 

    He replied: 

    If he catches up with part of 
    the adhaan, then the more correct view according to many of our companions 
    is that he should start at the beginning until he catches up with him. The 
    other view is that he should only respond to what he hears, and that he does 
    not have to repeat what he missed of the adhaan, and perhaps this is more 
    correct. It seems that this was stated by our Shaykh, Shaykh Sa’d – i.e., 
    Shaykh Sa’d ibn ‘Ateeq (may Allaah have mercy on him). 

    Those who say that he should 
    start at the beginning, if they establish proof then their opinion should be 
    accepted, otherwise the apparent meaning of the phrase “when you hear” has 
    to do with what he hears. 

    Moreover there is an issue 
    here: if he sees the muezzin but does not hear his voice, or he hears the 
    sound but does not understand what is said, then it is said: he should 
    repeat the phrases, because of the apparent meaning of the phrase “when you 
    hear”. And some of them say that he does not have to repeat it, and this is 
    more likely, because he does not know what to repeat because he is not 
    hearing what the muezzin is saying, but he knows that he is giving the 
    adhaan. 

    Fataawa
    wa Rasaa’il al-Shaykh Muhamamd ibn Ibraaheem, 2/134, 135 

    And Allaah knows best.