Use Assets : Importing and Exporting : Maintaining Category Assignments
   
Maintaining Category Assignments
The most important thing to know when you are exporting records to be imported into another catalog, is whether the new catalog already has the categories to which the records are assigned. If it does not, the categories assigned to the imported records will be created. But categories of the type “Folder” lose their type (assignment to the Source category tree). They are created as normal categories. If you want to keep the type of these categories, you must first export and import the categories.
Remember that it may be easier just to drag and drop records from one catalog to another, if both the source and destination catalogs are available to you. If they are not, or you are moving thousands of records at a time, then the export/import route is the way to go.
NOTE: When exporting records from one catalog and exporting them into a different catalog, the category assignments from the old catalog are always maintained and missing categories will be created. With drag & drop, however, you can choose if category assignments are maintained or ignored. If you choose to ignore them, missing categories will be ignored, too.