@Chèvre, Lorin,Thanks for posting in Q&A.
From your description, I know that you want to authorize an app to save files in the Android device's memory.
Based on my researching, if you want an app save file in Android device's memory, it is dependent on device storage permission, here is an article you can refer.
https://developer.android.com/training/data-storage/
Non-official, just for reference.
Moreover, if you want to manage the app via Intune, you can use app protection policy, however the app should be in the official list of Microsoft Intune protected apps or be integrated with the Intune SDK or wrapped by the Intune App Wrapping Tool.
https://learn.microsoft.com/en-us/mem/intune/apps/app-protection-policy-settings-android
Hope above information can be helpful.
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