The Unauthorized License Detected warning should show up if you are using an illegal version of eM Client, which is detected by your System checking eM Client's program file signatures. Recently, some users encountered this warning even with a valid program and license, because of an outdated certificate in their device.

To check if you are affected by this problem, please check this webpage: https://trusted-root-g4.chain-demos.digicert.com/
If the page shows a warning, you need to update your root certificate DigiCert Trusted Root G4.

This can be sorted by installing available security updates for your Windows or you can find the updates manually here: Support for urgent Trusted Root updates for Windows Root Certificate Program in Windows

You can also manually download the certificate here: 

DigiCert Root Certificates | DigiCert.com

Direct download for DigiCert Trusted Root G4 | DigiCert.com

To avoid similar issues in the future, make sure you have the Windows Root certificate AutoUpdater active.
This can be changed in Windows registry directly in HKEY_LOCAL_MACHINE\Software\Policies\Microsoft\SystemCertificates\AuthRoot
Just make sure the DisableRootAutoUpdate key is set to 0.