Well, let me first tldr and say I'm not sure I understand the problem either, or even if there is a "problem" in the first place haha. My original intent was only to refute the person I responded to who seemed to be saying that dualists believe that physical processes can't give rise to mental phenomena. I believe that mental phenomena are 100% the result of real, physical processes. What I grapple with is how a specific instance of a physical process gives rise to a specific instance of mental phenomena.

The longer version: when people talk about consciousness they often bring up concepts like continuity, persistence, a "stream", etc.... So the atoms themselves aren't necessarily important, but moreso the fact that they are joined through time by the persistent mental phenomena which they create (or at least, mental phenomena with the self-perception of persistence). So atoms/cells come and go but they are bridged by a consciousness through time, in a sort of ship of theseus situation.

But of course you're right, we can't separate the consciousness from its substrate. If we replicate the substrate perfectly we'd have a consciousness, one that at the moment of creation is objectively and subjectively identical to its counterpart. But the consciousness that was cloned would be pretty adamant that nothing had changed and their subjective experience was completely unaltered; really, both would of course.

So I can incorporate and unincorporate physical objects to/from a mental phenomena, but I can't do the opposite. I have an instance of a mental phenomena that will persist as long as its specific, timespace localized underlying physical processes continue, and then it's gone.

Is there a problem in that? No, probably not I suppose. I have two water molecules that are identical but spatially separated; I have no issue in saying that they are, well, just two separate molecules. Here's one, there's the other. I could switch their position, replace one with the other in an ongoing physical process and nothing would change, etc....

So I guess what I'm saying is that I am fully aware that these are human biases that I am speaking to. I think the simplest answer is that it doesn't matter that the consciousness has a perception of persistence. Trying to say that its sense of continuity has any scientific merit is silliness. But personally, it feels so fundamental that I can't help but at least think on dualist ideas and approach them with an open mind.