I guess it would sound like this:
Police: "Ok, Miss...uh, er 'Barista", up against the Expresso Machine, yur under arrest for Closing Early!"
Brady said:This is not theft.
It is almost always a bad idea, and may well cause significant loss of future income, but it is not theft. Theft is consciously taking money out of your till and pocketing it. Closing early is at worst laziness and negligence. Lets keep some perspective, eh?
Don't believe me? Call the police and try to have your employee charged with closing early.
Just echoing what others are saying: If it is a policy that has been put in place, and communication is open about not closing early, then yes, the person violated policy on numerous occasions and has to be let go. If this is not a communicated policy and something that you "just think would be obvious" then you cannot let the person go without a warning, IMO.
Perhaps the person was just trying to save you money? Sounds weird for an employee to think like this, but if the employee feels like they have ownership in the company (usually a good thing) then perhaps they were trying to save you some dough. Sit down and talk with the employee about it and make your policy clear. If the policy already was clear, then I think you know what you have to do.