Can we differentiate between the linear nerves (in/out signals across purely peripheral nerve lengths, inclusive of nerve-chains and possibly consolidating/distributive trees towards/from single roots) and networked nerves that do the cyclic bits (primarily, but not solely, in the cranium) of purely internal nerve-based feedback.
Replace the peripheral nervous system all you want (especially if it's to add back on the full function of an amputated limb, and let's skip over whether it's correcting an injury or a replacement towards transhumanism), that's just making things better for the rest of the body. It's just a matter of signalling. Ideally at the right speed/time-delay, too. Even if less than the replacement optimum - crank it up later, as well as gradually adding sensitivities and ranges, to get the reactions (both ways) adapted without the clumsiness of the young toddler or the old codger, unsynched or desynched.
But start messing with the 'processing' bits, in the truly central(ised) nervous system, and you're treading heavily. For one thing, it's more complex than detecting something (a sense or a desire to move, electrical or chemical at either end) and passing it on. However far up/down the chain or tree. Now you've got to replace it with a comparator. (Let's assume replacing one to one, because that way we're not multiplying the complexity of an already amorphously variable component.)
And if you match your replacements perfectly enough (functionally, one by one) then you're going the way of the Ship Of Theseus. Then things get weird.
Even more weird if you imagine it's possible that if you've got a way of progressing through the original nerves, in turn, analysing what and how to replace them with... Then, as well as actually replacing it, also slot another copy into the collection of previously-separately-copied 'replacements' that you've got sitting on another table (or simulated in a computer!) , keeping it supplied with build-edge transfers of impulses detected during the attempt to copy the original's reaponses.
You'd potentially have a second brain, by the end of the process, thinking the same thoughts. Or as many of the same thoughts as you'd allow it (staring out through its duplicate eyes, it could likely tell it was 'cogito'ing from the alternate location, ergo secundi, if you didn't purposefully deceive it).
Or how about what you do with the extracted biomatter? Can it also be done carefully enough to be reassembled, in a cradle of surrogate interfaces (and other messy biological provisions) to generate a third copy. Arguably the copy most like the original by virtue of being all the original bits, even!
Or at least that's all within the limits of your already marvelous ability to effectively wholesale replace(/relocate) wetware that is designed by time, and honed by its plasticity, with your (presumably) silicon-based replacement modules. But for this thought(s!) experiment, one has to assume the clever stuff is done and dusted. Much as with the problems of Transporter technology, in a different branch of speculative fiction. (Although there was that DS9 episode with Vedek Bereil!)