Not easy. You could ask him to show you the evidence of his military service that should include some form of discharge book or certificate of service, soldiers used to get a discharge book, (an AB108), officers will have their copy of The Queen's Commission. Tell him it is company policy to fully check the military background of all applicants as some of your work is of a classified or sensitive nature and do you have his permission to check with his regiment/ship/ squadron etc? Could he supply you with two service references please?
If you already have any genuine ex service people on your staff it would only take them about two minutes in the bar to uncover him if he is a Walt.