Don’t worry. Papaya FM automatically records every audiobook as well as either of its chapter you are listening to.
When you reopen Papaya FM every time, the player at the bottom side of the Discover page displays the audiobook and the chapter you were listening to when you exited the app last time. And you may tap the player and continue listening to the chapter.
In addition, all your listening records can be accessed to at the Recents of My Library. Please follow the instructions at Where do I Find My Listening and Downloading History to assess to your records, searching or continuing listening to the audiobook (s) you are or have had listened to.