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I think you can use `pulumi stack export`, trim the file to describe just the bits you want to move, then `pulumi stack import` on the other end. <https://www.pulumi.com/docs/reference/cli/pulumi_stack_export/>
Finally, tidy up the first stack using `pulumi state delete` (not `pulumi stack rm`, oddly...)

There might be an easier way. I admit that I've never done it.