This is probably a stretch, technically I think we'd be talking about an export/import.
Our company has two JIRA production environments for different business units. Would there be any way to Move an Issue from one environment to another with a post function?
Some scripting add-ons maybe able to do it. If your 2 JIRA instances are linked (application link), take a look at the "Remote Copy" feature in the "More" options of an issue, this might not be exactly what you want but it's pretty straightforward and a native feature.
While technically "unsupported", Atlassian uses this plugin internally, so it is relatively well maintained. It is also open source, if that is of interest to you:
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