If you are having problems with fingerprint reader on your Surface Pro 4 Type Cover with Fingerprint ID, see Troubleshoot problems with Windows Hello on Surface.
The Surface Pro Type Cover with Fingerprint ID works with all Surface Pro Devices running Windows 10, except for Surface Pro (1st Generation) and Surface Pro 2. Here's how to test Fingerprint reader.
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Go to Start  > Profile Image > Sign out.
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Then attempt to log back in using Windows Hello via fingerprint.