if u r unsure whether u prayed or not..its good that u prayed fajr again.
but brother, if u find difficulty in remembering that u prayed or not...write it down in a paper.
after few weeks, inshallah u'll remember by urself u prayed or not. no need to write it down then.
Do you know If he MUST repeat the prayer? Cause I to suffer for the same problem..sometimes I forget If prayed this prayer or not and its well kinda tiring to repeat the prayer