Use APKPure App
Get APKShare old version APK for Android
Extract and share you installed apps' APK
APKShare lists all installed apps (system and user) and lets you send the original APK file by e-mail, or share it with Android Beam, Bluetooth, etc.
Root access is not required and no permission is used.
This app is free software: the source code is at https://github.com/bparmentier/APKShare.