If it can be done, it will be. There are worse examples of man's perverse urge to satisfy his curiosity. The atomic bomb for instance. The next technological leap from transplanting the brain would be to copy or download the mind itself. That would involve mapping the circuitry and structure of the brain. It would also require an understanding of how and where memories are stored. They don't really know, but they are starting to understand how in molecular brain research. And if you cannot die, if your body can be replaced with a new one when it is worn out, then the universe is no longer infinite. The distance from one continent to another used to a prohibitively large, but today it is 6 or 8 hours away. This is what technology offers.
Can you imagine the medical, scientific, physical, metaphysical, philosophical, religious, ethical, moral, economic and political implications of all this?