Sorry for the delay in replying. Yes, you are the first.
Below some instructions for you.
To make update from v 2.2 Pro to last version you need uninstall previous.
For this need make FULL EXPORT of your books, delete v 2.2 Pro, install new version and then make FULL IMPORT.
This way of updates connected with Joomla 2.5. There is no other way update our component on Joomla 2.5
So, I propose you: make full backup of your BookLibrary v 2.2 Pro and make update in this way. Make all this first on a test website. And Main make: Full backup of your BookLibrary v 2.2 Pro before make any changes.
Or you can contact us through our contact form and ask about customization service (update BookLibrary 2.2 (on Joomla 2.5) to 3.5).