Hawking does not need to be mistaken about the brain in order for an afterlife to exist. If we are indeed nothing more than a particular arrangement of atoms, nothing in physics prevents one day re-assembling atoms into that same arrangement given the necessary technology (something like a molecular 3D printer) and the information necessary to do so. How to retrieve that information from history is the tricky part, but a plausible method is explained in this story: https://www.inkitt.com/stories/scifi/244915