How do the police verify the authenticity of an online profile? What methods do they use to determine if a profile is real or fake?

Sending unsolicited, directed messages to someone isn’t a crime.

Without an articulable crime, law enforcement is unable to obtain the Federal Grand Jury Subpoena required to compel Facebook to provide the specific information necessary to even begin to trace where the person is operating the fictitious Facebook account from.

Whatever happened next with that matter occurred outside the “know” of my pay grade. All I know for sure is that my Lieutenant didn’t get fired, I’m very glad I was not fired or demoted, and the constitution still protects people's rights to create and operate a fictitious online profile.

Has anyone who has been a victim of a narcissist made contact with the other victims of the narcissist? Did it help to confirm what you suspected about the narcissists?

… However, if the department were to file a civil lawsuit against this mystery individual for something akin to Defamation of Character, “Facebook” could be named as a co-defendant and might be willing to provide the information we need… and then repeat the process to compel the Internet Service Provider Mr. Imposter subscribes to to disclose the street address and billing information of whoever pays for the service there. (If it came back to a smartphone, we’d have him virtually dead to rights.)

As I am the resident Computer Crimes Specialist in my department, the Chief called me up to his office, where darn near everyone in my chain of command was present, and he assigned me directly to find out who this imposter was and string him up in every way legally possible. So suddenly, I was the one having the difficult and awkward conversation with the Chief (in front of everyone on who has direct influence over my career):

Unbeknownst to him, one of the people he clicked “accept” on was some “cop wannabe” who had been harvesting my Lieutenant’s photos and consumed everything that was posted on his page. When my Lieutenant deleted his account, this mystery person created a NEW Facebook profile using my Lieutenant’s name, RE-populated the page with all of the content he took from the original, and began impersonating my Lieutenant. My Lieutenant learned of this when he was confronted by the parent of a 17-year-old boy in a neighboring town, this parent furiously took issue with the very inappropriate pictures of near-naked men that were being “direct messaged” to that boy by the person impersonating my Lieutenant. My Lieutenant immediately went in to have a very difficult & awkward conversation with the Chief of Police.

Is a man over 50 not married no kids a red flag?

“The bottom line is, Chief— and I fear that I may get fired or demoted for saying so— but this heinous act against my commanding Lieutenant isn’t something that we, the police, have the power to pursue, because of the First Amendment.”

My Lieutenant is not only the commander of the Criminal Investigation Division, he is also the commander of my department’s SWAT team. One day he decided to “try out” Facebook. He put up cool pictures from different SWAT callouts, training, and pictures of himself in various uniforms. And he wrote a decent Bio, made a couple of posts, clicked “accept” on the “friend request” notifications a lot… but after a fairly short time, he decided it was not really for him. So he killed his account & didn’t think much more of it.

Extreme Example:

Blocking Brain Inflammation Molecule May Halt Alzheimer’s - Neuroscience News

Without there being some kind of Court Order forbidding the behavior, sending unsolicited pictures of young, fit men in boxer shorts to anyone isn’t illegal.

Making a Facebook profile under a pretend name isn’t a crime, even if the person you’re pretending to be is a real person. You can’t go to JAIL for that, it isn’t a “police issue.”

I understood my Lieutenant’s pain, and also my Chief’s rage, and I appreciated how frustrating and embarrassing this was for my organization, so I was very pleased to have been able to add:

Was Jimmy Carter a good President of the United States?

Downloading pictures and copying text from a publicly accessible source, such as from a Facebook profile (that you have been allowed to view because the “owner” clicked “accept”) is not a crime.

In the USA, people’s online activities are affairs protected from criminal prosecution by the First Amendment of the Constitution. That’s right: what you post, pictures you publish (provided they're not child porn), opinions you share, the name you say is yours, etc. etc. is a right that you have that all police officers in the USA are sworn to uphold. “Verifying the authenticity of an online profile” is not something the police do.