Conscious AI hypothetical

Suppose we have a conscious computer program; a program which, when executed, is conscious. We save the memory states and IO from the program at every stage of its execution, and then replay each state, one by one, on a second computer, without actually executing the program. Is the second computer conscious too?

In other words, if a computer is conscious, does its consciousness derive from the instructions it executes, or from the series of states it transitions between?

Conciseness, as most of you define it here, would simply be the result of having the need for something to produce adequate models of the future as based on previous experience.

To produce such models the apparatus producing it must include itself in those models if it wishes to interact with the outside world in the future that it imagines.

The several iterations of the latter produce in our minds "the self".

Natural selection (as a feedback loop) has judged the beings with an adequate amount of these models to be quite successful at our scale.

Of interest here is that any further complexity which leads to "the self" being able to get lost in those models instead of forgetting to simply use them to better interact with the surrounding world leads to neets/philosophers etc... which ultimately leads to the lowered chances of passing on the gene set with a heightened likelihood of producing more of such individuals into the next generation.

TL;DR: "the self" is an illusion... or is nothing special to say the least; if one ever had to solve "the /chech/PARADOX!" -- we all know what we would choose.