Is the fast valid if I intended to fast two hours before Fajr, then repeated the intention after the Fajr adhan?

If the intention to fast crosses your mind at any part of the night, then your fast is valid, and your intention at the time of Fajr prayer is considered effective. Ibn Taymiyyah said: "Whoever has it cross his heart that he will fast tomorrow, then he has intended." So, a mere resolve to fast is sufficient to fulfill the required intention.