Hello Warren,
If it is a hosted image service in ArcGIS Online, you can try using ArcGIS Assistant Beta to copy the service to another organization.
ArcGIS Assistant is a community driven project and not an officially supported by Esri Technical Support. Check out the FAQ and the Discussion Forum on GitHub.
This Read more about it here: ArcGIS Assistant Beta (tool for managing content a... - Esri Community
Another method would be to do manual download/export and then publish the imagery data to to another organization.
Best regards,
Kanin
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