To transfer iBooks to a new device, you need to first log in to the iBooks app.
On the top left of the screen, you'll see "Store", click on that to be brought to the iBooks store.
On the bottom right corner of the screen you'll see a button labeled "Purchased", click on that to view all iBooks currently linked with your account. From that screen, you'll be able to download all iBooks currently linked with your Apple ID. To download, click on the cloud icon.
If you are still having issues please call Apple Tech support at Please contact their support team at 1-800-275-2273.