In A Separate Peace, Leper signs the telegram he sends to Gene, “Your best friend.” Why does Leper do this?

Leper isn't one of the more popular kids at Devon.  He
appears to be secure with his loner status, preferring to be one with nature rather than
in the center of the social circle.  After the war, however, we see a different Leper. 
His yearning to be accepted by his peers is more evident and he shows envy toward the
closeness some of his classmates, like Gene and Finny, share.  He reaches out to Gene,
perhaps because he thinks he can take Finny's place as his "best friend".  Leper's
experiences in the army makes him realizes the importance of friends for the first
time.  He is desperate and needs someone to talk to, so he dumps his troubles on Gene. 
It's possible he uses "Your best friend" to guilt Gene into helping
him.