Is it possible to sync the current position / page of an EPUB book between two devices?
Check out PageTurner on Google Play. It's supposed to do what you want, although there are some mixed reviews. It's worth a try though.
PageTurner is an open-source e-book reader that allows you to sync your reading progress across devices, without needing a DropBox or Google Drive account... just enter your e-mail address and it works!