We've been dumping our Zephry test cases into Testrail - so I know enough to help here at least.
You go into the Zephry interface in your space - and export test cases - you will likely need to re-import "that" back into your Jira as an additional/add/edit.
You MIGHT be able to do it all in one shot - check the interface to see if it can grab all the fields in your tickets.
If you end up getting a partial dump - only zephry goodies and not the ticket meat - do an export of the tickets and use the jira-admin side of importing to "merge/write" - not overwrite/add.
I don't know the exact process as we're "moving out" - but I suspect the key to your success is the Zephry interface.
You will need to contact their support to get further information - be warned - its a bit hectic - they had a rough week. (Full outage - we reported the issue too - ha ha ha)😅
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