Login User To Web Application if User Logged In in Dekstop Application

Scenario:

I have a desktop application which is working fine with its database from where we authenticate user using Username and Password, we have a web application that also requires same credentials for logging in.

What i want to achieve is if User is already logged in on Desktop application, i need to skip the Login part on Web Application when user opens it. Web Application gets launched in browser from a button inside my Desktop application using Process.Start() thing.

One way that is is my mind is to pass username password in query string and using java-script putting username and password in fields and posting form programmatically but it is not safe as user can save username password from query string and can use it on any system to login which is not secure.

Any thoughts on it what are my option to do this type of thing?