Time limits for reporting the injury are pretty flexible. it may depend on when the employee knew he was injured or knew tht the injury was work related or knew he might be entitled to workers' compensation benefits. This is an issue you should be discussing with your workers' compensation insurance carrier. That's what you pay them for. If they feel it appropriate, they will investigate and determine whether to accept or deny the claim.
Generally the longer the employee waits to report the injury the less likely that the workers' comp carrier will accept the injury, although there is no specific time limit within one year of injury.
If the employee went so far as to have surgery, yet not report the injury, your carrier (or the employer, if not insured) will likely investigate and contest the compensability of the claim.