If you have a wireless network and sharing of the library folder is enabled, there is an easy solution to transfer your books. Install ES File Explorer (free) on your Fire. With your host computer on and wifi enabled on the Fire:
Tap on the "LAN" tab, => Menu => New => Scan => An icon with IP address will appear. Simply tap on it, (enter your host computer's password if required) and drives/folders from the host computer will appear for transfer from the computer => Fire.
I use this method routinely on all my devices, from any room in the house with no need to connect with cables. At least this is an alternative until you solve your problem. BTW, ES File Explorer is the best, IMHO, and a must-have app on any Android device.
Of course, you may also move files via the cloud, i.e., Dropbox or Box, but it is more cumbersome.