Have you authorize both devices with the same Adobe ID?
I'm having the same problem moving library books rom my pc to my Nook. It says I don't have permission but I've done it in the past. How do I find out about the ID?
Start Digital Edition. Press Ctrl + Shift + I. In the Windows was open you found the Adobe ID do you used.
To found the Adobe ID in your Reader check the Help-Document of your Kobo-Reader or ask by Kobo directly. I have a other reader so i not know this.