Answered by Shaykh Ilyas Patel
Just to clarify: Is not permissible to make nafl in the entire time of Fajr or just after one has prayed the fard of fajr to the time it expires?
In the Name of Allah, Most Beneficent, Most Merciful,
It is not permissible to perform any nafl salaah during the entire time of Fajr, nor to after one has prayed the fard of Fajr until the time it expires.
It is mentioned in Maraqi al Falah that:
“It is offensive to perform nafl after the true dawn (beginning of Fajr time) more than the sunnah of Fajr, before performing the fard, because the Prophet (Allah bless him and give him peace) said, `the ones who are present should convey to those who are not present. Know! There is no salah after true dawn except two rakats [of the sunnah of Fajr].’ ” [ Hashiya al Tahtawi ala Maraqi al Falah pg 151 ]
And Allah knows best.