If as you mention the "hacker" chatted with you via the Facebook website, then all you will get is the IP of a Facebook server somewhere in the cloud, which won't help you much.
Only Facebook could get you the sender IP, and I don't believe they would disclose such information.
Moreover, the attacker probably used at least one proxy, which would make your found IP pretty useless, unless you force the proxy to disclose the information as well, which will be extremely difficult.
If harm was made, besides contacting relevant authorities, not much can be done in your case. If the harm is high enough they might contact Facebook but many such cases are dropped (for example in Belgium where I live there are so many claims that, if it does not concern terrorism, pedophilia or money laundering, chances that priorities due to lack of budget will end up in no followup)