Promoting the user to trust level 3, and making sure that the trusted users can edit others setting is enabled on your site would probably work for this. The user will be able to recategorize topic to and from any categories that they have access to on the site.
For more details about how this works, and the difference between what trust level 3 and trust level 4 users can do, have a look at [retired setting] What does the "trusted users can edit others" setting do?.