My phone has a fingerprint scanner. I notice on the Google Play Store, it has the option to verify your identity with a finger print scan instead of typing in the password when making a purchase. Does this mean Google has a record of your finger prints? When is this record made, when you first enable the screen lock with your finger print?
No, your fingerprint data never leaves your device.
Your fingerprint data is stored securely and never leaves your Pixel or Nexus phone. Your fingerprint data isn't shared with Google or any apps on your device. Apps are notified only whether your fingerprint was verified.
Source is from Nexus/Pixel support pages hence why it mentions them specifically. The same should apply for other devices however)
When you activate the fingerprint authentication for any third party app what it does is that it asks your Android system to initialize the fingerprint hardware which checks for your fingerprint. And if it matches it passes that information back to the system and then to the app. The only information that the app gets is that the scan was successsful. You fingerprint never finds away into the app.