This is a hard one to process. First, I want to know why the instructor would accuse you of theft. How would he know that the headphones weren't yours? Was there a procedure you're supposed to follow?
To tell the truth, I've salvaged a number of things from the lost and found can at my daughter's school. You'd be surprised what kids lose or throw away, including a $300 flute, a violin and some really nice jackets.
So I personally ding you too hard for something I would have done, but I can't advise well on how others might react.
Your best bet is to A) fight it tooth and nail and B), if you lose that fight, explain it fully in the appropriate box in apps, and hope screeners see this as, well , kind of a ludicrous charge.
I also have the nagging doubt that there's more to the story than OP is letting on.