Stealing the physical menu(s) is wrong, and a crime. That is for sure.
But a restaurant having cameras positioned like this, and posting the footage on public social media seems like a foolish strategy that could backfire on them legally. If they have filed a police report, why go to these lengths? Also, it could cause others to copy the copycats, if that makes sense.
And I'm unsure how someone's online payment record could lead to being found to be a restauranteur in another country. Something here smells wrong. I reckon there's more to this than we know.