The user has advanced searches defined and saved in in a test system and would like then migrated to the production system.
If an Advanced Search is defined for a test system, how can it be migrated to production without rebuilding it?
There is no mechanism to move just the advanced searches, but you can use the export/import feature under General Administration--> Configuration to move all of the customizations from a test system to a production system, which includes the advanced searches.
You can repeatedly do this if your production system was created from the restore of you test system and you then build the advanced search (or do any other customizations) on the test system first, and then apply it to the production.
If you don't follow this "do in test and then move to production" process then there can be problems. So much of the customization in UAPM is interrelated. You can't just move an advanced search because the fields in it may be customized based on the security role it is under, and this may be different from one system to the other if not kept in sync.