To move your library to a new system: the easiest thing for you to do in this case is to copy the Library Folder from your backup or another system of yours to your destination system. This way, you do not have to re-download all those GBs of sample data.
1. Copy the whole library folder over to the new system
2. Log in to Native Access
3. Find the Library in the “Not Installed” section
4. Click “Add Library” and point it to your copied folder
To move your library to an external drive: follow these instructions:
Native Instruments Instructions