[Manal]

There is no legal way tracing facebook user IP unless you do some illegal activities like sending him a fake link and when he click you will get his IP address easily.

Or you're from an LEA and you've got a subpoena for the specific user account. It would work

[PacPers]

here are some free email tracking services if you wish to do the email method

https://getnotify.com

https://www.free-email-tracker.com

They work by using a samll gif inside the email and if opnend you will get the user's IP. BUT some email providers block external images for this reason! AND it will only work if they have the email account listed in their profile.