Yes, but you need to follow the due course of law, such as issuing a show-cause notice, allowing the employee to respond in writing, considering the response, issuing warning letters for the first misconduct, and then, after a repeat of the behavior, conducting a fully documented inquiry, etc., and only then proceeding with termination. I don't see any mention of a warning for previous misconduct. That should always be in place before termination.
This is because, as a cashier, the employee would most probably be a non-supervisor and could challenge the termination. The labor courts are labor-friendly (meant to protect employees' rights) and will quash any termination not done as per the prescribed procedure.