My answer to that philosophical quandary is very 40k in nature. I believe everything has a metaphysical spirit. The soul may or may not exist, but this spirit transcends any religious belief and isn't truly scientific in nature.
It's something that everything that has ever existed or ever will exist has. It's what makes each individual item, from each living creature to every rock, to every river unique. It isn't the composite parts of the item that does this.
Take your phone for example. It indeed does have a machine spirit. That spirit is what makes it the phone you know versus anyone else's phone. You can replace every part within it over the years but the phone remains. Your memories with it will remain and that bond you share creates maintains this spirit. No matter what it will always have this spirit and it cannot be destroyed.
Humans have this very same spirit. As long as my identity exists, as long as my ego remains. I remain me no matter how much of my flesh sack remains.
I'd argue yes. That is until each are refined on their own to form in to their own souls split from the same one. Much like a cell, when it splits, forms two others down the line. Just at a MUCH slower rate.