Ok well first of all, good for you to have the courage to confront him. Now if he is willing to admit the crime on Facebook, perhaps he is willing to confess the crime to police? Did you ask him that? If he is truly remorseful, he may indeed be willing to do that?
Now in Australia, the burden of evidence can sometimes be very 'lite', its not like America at all where you actually need real evidence to get a conviction. I have seen plenty of cases of people convicted in Australia based on evidence that would be classed as 'circumstantial' in America. So it can be much easier to get a conviction in this country without much evidence at all. So the point is, you have nothing to lose to report this to police and see what happens?