Yes, the purchases are associated with your account and is valid in a single store (Apple AppStore, Google Play, etc.) for an unlimited number of devices.
If you need to install the app on a new device, you can login in the app store with the same account used for the purchase, and you will be allowed to download the app on your new device.
However, purchase is NOT valid in another store (e.g. if you have purchased in Google Play, this purchase is valid only in Google Play and it’s not valid in Apple AppStore).
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