QUOTE
Remus must be above suspicion, either because of his lycanthropy or for another reason.
^That's the only requirement. Whether Remus decides to confess his sins or not is totally up to you. It's your story; you may end it however you like.
Would Remus admit it or would he be happier keeping it to himself, satisfied that he's even more devious than his mates as well as being better able to avoid discovery or worse, detention or expulsion?
Remember that he was a Prefect at some point, in any or all of his 5th - 7th years.