Viviane, a burst of activity in the brain doesn’t explain the phenomena as the memories are not there to stimulate by such activity, as it is brain destruction that is the very thing killing dementia patients. Also the experience of brain states does not mean that whatever is experiencing those states is in the brain. Indeed consciousness itself is entirely anecdotal.
Finkelstein, it might be better to get evidence first of all of what consciousness actually is, as opposed to correlates of consciousness found in the brain. I can provide any amount of different forms of anecdotal evidence that consciousness is non-local to the brain, which is but one minimum requirement to a soul living after death, but that probably won’t be good enough for some, even though the same is also true for consciousness itself being real as opposed to an illusion. Anecdotal evidence that consciousness is real is all there is in terms of evidence that it is real. Looking at a brain wont prove anything about the reality or lack thereof of where of what does the experiencing.