Evidence of reciting the Quran loudly while making up the Fajr prayer during the daytime
14-1-2014 | IslamWeb
Question:
Should making up the Fajr prayer after its due time be made loudly?
Answer:
All perfect praise be to Allaah, The Lord of the worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
Whoever misses the Fajr prayer until its due time is over at sunrise has to make it up and recite the Quran loudly so that when he makes it up it is as if he is performing it in its due time. There is no difference between performing it individually or as an Imaam (i.e. leading people in it), based on the Hadeeth narrated by Abu Qataadah 
regarding their story when they overslept and missed the Fajr prayer: “Then Bilaal gave the call to prayer and the Messenger of Allaah, sallallaahu ‘alayhi wa sallam, prayed two Rak‘ahs. Then, he prayed Fajr and he did so the same way he did every other day.” [Muslim]
His saying: “… the way he did every other day” indicates that the way in which missed prayers are to be made up is the same in which they would normally be done.
Al-Majd ibn Taymiyyah 
said, after mentioning the previous Hadeeth: “It proves that making up the Fajr prayer during the daytime should be made loudly.”