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.