Getting copied from a frozen brain into a computer is a pretty drastic change, but suppose instead it were done gradually, one neuron at a time. If one of your neurons were replaced with an implant that behaved the same way, would it still be you? A cluster of N neurons? What if you replaced your entire brain with electronics, a little at a time?

Obviously there is a difference, and that difference is significant to identity; but I think that difference is more like the difference between me and my younger self than the difference between me and someone else.