There's no way for you to sync the book purchased to another computer, however, you should authorize the laptop, then to transfer purchases, it may be transferred to your laptop.
And if you use leawo itransfer to do that, it is surely can help you to transfer the book from iphone to laptop by just drag and drop, or select the book on it and right click it then to choose "transfer to computer".
Get this
iPhone to Computer Transfer from CNET.