Audible today updated their official Windows app to v10.3.12. This update brings the ability to sync your Finished status between devices. The changelog reads:
New in 10.3.12:
Sync your “Finished” Status
When you mark a book as “Finished”, it syncs seamlessly across all your devices and platforms.
With Audible app, you can download over 250,000 professionally narrated audiobooks and periodicals to your device.
Find the updated app in the Windows Store.