Facebook is full of cases where accounts have been hacked, or it could simply be that someone registered under Facebook using false details. I don't use FB so I don't know how they carry out ID checks on new accounts, or even if they bother.
But the answer is Yes. You ask for help, but there's nothing we can do here for you.
If you have any issues with slander via FB then you need to contact FB themselves and state the situation. As to your job, I can't offer anything at all. I would have assumed that some sort of disciplinary procedure was followed and if so, you or your representative would have been able to present your side of the story.