Let us assume that someone sends me a threatening message on Facebook. I also want to assume that they have used a VPN to do so, given the location I got from an initial trace is looked into and is false.
I think you are misunderstanding some important details. Most importantly, any attempt to trace the facebook message will not trace the user: just Facebook. Facebook is not a peer-to-peer chat network. Both of you communicate with a central Facebook server, which means you have no way to track the end-user.
As a result, they don't have to use a VPN to hide from you. Facebook is already hiding them. Facebook might be able to track the user (in fact, I'm sure they are commonly requested to do so by law enforcement), but in the event that a VPN is using, Facebook would likely just track the user back to said VPN.
So, without delving into the realm of the probably-illegal, there is nothing you can do to track someone contacting you through Facebook messenger, and Facebook certainly won't do it for you (nor can they necessarily do it if the person is behind a VPN).
There are other questions on this site asking about tracking people behind VPNs, which would be applicable in this case. You could start here, keeping in mind that this is venturing into the probably-illegal and also not-for-your-average user:
