In a world which to a visitor coming from our own world would appear to be identical to our own, the mental processes (thoughts, emotions, memory) do not occur in the brain. That is, memory isn't stored in the brain and it is not the brain that is "doing the thinking". Instead the brain is a receiver for information passed to it from the incorporeal soul, in the same way that a radio receiver receives a radio signal.
I already said the world is identical to ours in all respects (except that thoughts don't happen in the brain), but I want to emphasize the following:
To the scientists of that world, when they use current medical imaging methods like MRI, PET, EEG, and whatnot, the brains of people from that world look identical to brain activity images of people from our own world.
The people of that world hold the same beliefs as we do. That is, some do believe in a "soul", but there is no proof for it, and most scientists believe that the soul and telepathy are superstitions. Scientists of that other world, like scientists of our own, believe that memories are stored in the brain and that thoughts originate in the brain, and they interpret images of brain activity according to those beliefs.
There is no measurable electromagnetic or other "transmission" from or to the brain beyond the well-known electric activity of the brain itself.
In that other world, the soul and the brain exchange information in a way that current technology (in both worlds) cannot detect.
What observation would prove to a scientist that the brain is receiving thougts and memories from outside instead of thinking thoughts and storing memories within itself?