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 is His slave and Messenger.
The mention of Allaah said in the morning is among the mention which is restricted by time, and its time starts from the beginning of the morning; the evidence about this is the saying of the Prophet "when he has reached the morning", meaning when the morning starts, and the time of the morning extends until sunrise as established by the scholars . Therefore, the time of any mention of Allaah which is mentioned in a Prophetic narration restricted by being said in the morning starts at the beginning of the morning.
Therefore, it is permissible to say the morning mention of Allaah after the beginning of the time of Fajr and before the Fajr prayer, but its best time is after the Fajr prayer. An-Nawawi said: "The best time for the mention of Allaah during the day is the mention after the Fajr prayer."
Allaah Knows best.