A file should be saved automatically to cloud and only cache be saved in the device and also an option for offline saving should be provided to read offline. But basically saving to cloud will let you to acces the pdf from any device.And simultaneously refresh of history on all the linked devices and websites.
All the device should work as one rather than different it is ultimately same application opened by same people then, why extra effort in different devices.
This will allow user to download previously opened pdf anytime, anywhere and no matter how much we delete the app or close the page i can access my file in quick.