Yes, to do this you want to:
1. Make sure that your book is on the "reading" list. If it's not, click on the + symbol in the corner and add the book
2. If you are logging a session but still reading the book, "Add to Reading." If you are logging the book and it's now done, select "Archive." From there, make sure you add the date read, number of minutes read (if applicable), and mark "Count as completed" if the book is now completed!
NOTE: We are always making updates to the mobile app. In particular, we are working to make this more intuitive. Remember to always have the current version of the app to be up to date and have the best experience!