So Fletcher stole the music scores?

Yes I'm pretty sure that he did. He was constantly manipulating Andrew and testing him throughout, to see if he gets discouraged or rises to the occasion. So this could have been for Andrew's benefit to see if he can step up, or equally it could have been to test the other guy to see how he handles it. I think he rated the other guy to some extent since he explains to Andrew later that while Connolly(?) never really had it, the other guy got discouraged and left to pursue a medical career.