The manual is very patchy in terms of the necessary steps to transfer the content from the internal drive to the new SSD.
I proceeded as follows:
1. Insert JetDrive 520 (SSD module) in the external housing
2. Switch off the MBA and connect the SSD with one of the two USB ports
3. Option / Alt key at power button until the Mac starts up and displays a selection screen
4. Select the recovery partition by clicking on the corresponding arrow
5. Start the Disk Utility program after the Mac has started the base system
6. Delete the JetDrive 520 (Mac OS Extended Journaled) - Volume name does not matter is, eh overwritten equal
7. Restore the internal SSD (source) on the new external SSD (target), this content will be copied, including the recovery partition (has approximately 60GB occupied space lasted about 7 minutes)
8. Check and repair the permissions on the new SSD
9. Connect MBA off menu command and replace the SSD, the old SSD initially not
10. Start MBA and select in the Control Panel, the boot volume (thus the Mac starts up again rapidly. If you leave this step out, the Mac initially examined at the start the old SSD and starts after timing of the new)
11. Install JetDrive Toolbox (or another TRIM Enabler so fast TRIM function is used when deleting files on the SSD)
12. Enter at least for the Office 2011 license key (applies if necessary also to other software that the volume ID for licensing remembers).