with a fingerprint reader log directly into the screen?

Microsoft Wasn't Really Interested in Reading Fingerprints on Its Devices Windows 10 Mobile, even if this functionality is now present on the HP Elite X3, professional smartphone recently available.

Microsoft has also introduced Windows Hello on Windows 10 and the iris scanner on the latest high-end models Lumia but the upcoming abandonment of the range but fingerprint biometry remains rare on Windows 10 Mobile.

Microsoft biometrics patent

That may change soon, maybe on a future range Surface Phone. A patent filed by Microsoft indeed describes a fingerprint reading system operating directly via the screen of a mobile device.

Surface Phone

It would avoid having to integrate an imprint reading module into the design, making it possible to imagine refined form factors. The system can work with LED displays but also with AMOLED screens.

Of course, it is only a method described in a patent and nothing says that it will be applied in a concrete product but at the same time, it could well enter the configuration of mobile devices intended professional.