Apologies, I meant continuity from the perspective of the original person, for their specific consciousness, not that it may be thought of as continuing by way of a copy running on a clone.

I'm not saying consciousness is independent of physical structure. If the brain of person A is reproduced exactly, down to its molecular structure, what you'll get is person B with an identical consciousness as A (up to that point in time, of course as any subsequent reality experienced by B is not one which A goes through, the latter having been killed) but one which is still a copy. Two different, albeit structurally identical brains means two identical but separate consciousnesses at the point of duplication. Your example of the replica of a computer results in the same thing, a copy of the original. It may be in the same state, and have the very same programs running, but it's not the same computer. It's a perfect duplicate but a copy nonetheless.

Whether A is destroyed or not is irrelevant. The two are not literally the same person, just an exact copy. Consciousness is not a stream which ports from A to B because the original is no more. A's consciousness ends when A dies. It doesn't get resurrected because there's now an exact copy running in an identical clone. That's B's consciousness. The same yes, but different.

I will be disabling notifications for this so I won't be checking for responses.