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Should be covered by Brain Uploading.
there is nothing on Brain Uploading that says the original has to die, the second bullet point in the description points out that having the process be destructive usually for convenience of the author of not having deal with the consequences of two copies running around and there are several examples that are not involve the death of the original
When a work of fiction has a digital copy of a character that lives inside a computer/datascape. I'm trying to refer to Data-Riku and Data-Sora from Kingdom Hearts re:coded, but I'm not sure which trope describes them best. Brain Uploading works, I guess, but the real Riku and Sora are still alive, after all, and there's not really any negative implications brought up from copying them.