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

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.