Ruling on responding to the adhaan recorded on the al-Fajr clock

It is not prescribed to
respond to the recorded adhaan, because it is not a real adhaan, i.e., it
is not done by the muezzin at the time; rather it is a recording of a
previous adhaan. 

Shaykh Ibn ‘Uthaymeen (may
Allah have mercy on him) was asked about the adhaan on the radio or
television: should one respond to it? He replied: 

With regard to this adhaan,
one of two things must be the case: 

(i)It is on the air, i.e., the
adhaan is being given at the time of prayer by the muezzin. In this case it
should be responded to, because of the general meaning of the command of the
Prophet (blessings and peace of Allah be upon him): “When you hear the
muezzin, say what the muezzin says.” But the fuqaha’ (may Allah have mercy
on them) said: If he has offered the prayer for which the call is being
given, he does not have to respond.

(ii)The adhaan is recorded and is
not an adhaan being given at the time; in this case it should not be
responded to, because it is not a real adhaan, i.e., the man is not giving
it at the time it is commanded to give it; rather it is an audio recording
of a previous adhaan.

End quote from Majmoo‘
Fataawa al-Shaykh Ibn ‘Uthaymeen, 12/196 

What is prescribed is for
you to give the adhaan in your house, so that you may attain the reward of
this great ritual, because of the report narrated by al-Bukhaari (609) from
‘Abd al-Rahmaan ibn ‘Abd-Allah ibn ‘Abd al-Rahmaan ibn Abi Sa‘sa‘ah
al-Ansaari from his father, who told him that Abu Sa‘eed al-Khudri said to
him: “I see that you like sheep and the wilderness. When you are with your
sheep in your wilderness, and you recite the Adhaan for your prayers, raise
your voice, for no jinn or man or anything within the voice range of the
muezzin hears the call, but will bear witness for him on the Day of
Resurrection.” Abu Sa’eed said: I heard this from the Messenger of Allaah (peace and blessings of Allaah be upon him).

It is also prescribed for you to respond to the real-time adhaan that is transmitted live on the radio or television, as stated above. 

And Allah knows best.