PLEASE READ THIS BEFORE YOU COMMENT, EMAIL ME OR PHONE ME. I'm only licensed in CA. This answer doesn't make me your lawyer, and neither do follow-up comments and/or emails and/or phone calls, and you shouldn't expect me to respond to your further questions if you haven't hired me. We need an actual agreement confirmed in writing before any attorney-client relationship is formed. This answer doesn't constitute legal advice, and shouldn't be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue.
The first answer is correct.
If the fake account were still active, it could be reported to Facebook https://www.facebook.com/help?page=798. Operating an account under a false identity is a violation of terms that should lead to cancellation of the account. That is a matter handled by Facebook itself.
If the fake account were in the name of someone known to the ex-girlfriend, and was therefore friended and granted access to non-public portions of her Facebook postings, there might be a claim for fraud - however, to be actionable such a claim would usually require either personal gain to the deceiver or injury to the ex-girlfriend.
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