I bet you're the perp, Unagi. Why else would you even know what's going on in your ex-girlfriend's life? :P
IPs are never very accurate and can be easily spoofed anyway. Plenty of free proxies out there. She needs to change all of her passwords to different things (not just use one for all). Make sure it is a long password with a combination of uppercase and lowercase letters, numbers, and symbols. Don't use actual words, as they can be cracked easily. Make sure she changes all of the security questions and answers on all services as well. Don't use things that are public knowledge, like mother's maiden name, first school, etc. Make sure that the failback e-mail (where lost passwords are sent to) is right. If someone has had access, they could have changed that to simply e-mail new passwords to them instead.
If all else fails, take the opportunity to ditch Facebook. It sucks, as all social networks do. Maybe also try getting a real e-mail address instead of relying on free, web-based junk?