The process of moving a library in Kontakt has changed with the update to 5.6.8. Instead of removing and re-adding a library you simply need to move the library folder on your computer and then re-link the missing libraries in Kontakt.
In this example we have moved the HZ01, HZ02, and HZ03 into a sub folder and once Kontakt is opened they will now display as missing.
If you click on the Locate button outlined in green above this will bring up a pop-up which is pictured below.
If you know where the library folder is moved to, choose Browse for folder which is outlined in green above. Clicking this will bring up a browser window where you can browse to the library folder (the folder ending in ...Library). Select the library folder as pictured below and confirm, you might be asked for your computer's admin password in order to make changes and then the library should appear in Kontakt.
If you follow these steps and run into issues please reach out to support and we will help troubleshoot this.