Sorry, "aby" was a typo that should have been "any".
First some background. iTunes has some anti-piracy measures built in that prevent a device that already has purchased media on it from syncing with a new computer. When you attempt to do this, you will be warned that iTunes will erase any purchased media currently on the device and replace it with the media in the iTunes library you are syncing with. While you could theoretically just download everything he has on his device now again, you would lose any app data (such as game progress) in the process of having his apps deleted then downloaded again. The assumption is that any iOS device will be synced with iTunes prior to adding purchased media to establish a syncing relationship between it and they computer it will be synced with.
In order to avoid this problem, prior to syncing with your computer the first time you will need to perform the steps outlined in this user tip from wjosten: Syncing to a "New" Computer or replacing a "crashed" Hard Drive (while this refers to iPhones, it's the same for any iOS device). Step 2 (and the corresponding reference to contacts and calendars in step 9) will only be necessary if he was syncing contacts or calendars with a different computer using iTunes. Assuming he wasn't (such as if he was syncing them with iCloud), you can skip this step. Step 4 refers to authorizing your computer for any Apple IDs used to purchased media on his iPod touch. If he was already using your iTunes store ID for his purchases you can skip this step too as your computer is already authorized for your iTunes store ID. At step 5, transfer purchases is now in File>Devices. Finally, since he hasn't synced any photos to his iPod from a computer, or added any music from CDs by syncing with iTunes, you won't have to worry about the reference to extracting these using 3rd party software.
What this will do is transfer his purchased media to your iTunes library, and allow you to sync his device with your library without any data loss (such as game progress). After doing this you can select your audiobook to sync to his device without any issues.
iTunes will keep separate sync settings for each device but you will want to review your sync settings prior to your next sync to avoid inadvertently getting his apps, etc., on your device. You will also probably want to uncheck "Automatically install new apps" at the bottom of the apps list in your iTunes sync settings as shown in the image below. This will prevent new apps and other media added to your library from his device when he syncs from automatically being added to your device the next time you sync (and vice versa).