IAP plugin doesn't save anything, it's your job to handle consumable and non-consumabe purchases in your game - for example, when an item is purchased, add it players's inventory and save between sessions. (either to local or to cloud storage)
Google Play and Apple Store keep track of purchases, and you can request "Restore purchases". But, of course, they do not share this data. It's again your job to keep track of purchases made on different platforms, if you want to allow players to play on multiple devices under one account.