I'm at a loss to understand how you might think the answer to this question could possibly be anything other than yes. Anyone "can ask" anyone to do anything. If your intent was to ask whether one of the hundreds of police departments in Florida might investigate a fake social media profile, that's not something the anonymous strangers at this site can answer intelligently. That said, I would hope it obvious that, in the abstract, fake social media profiles are not generally going to be of interest to most law enforcement agencies.
Are there perhaps facts that you didn't share that you think might make this a criminal matter in which the police might be interested?