Single sign on MVC to Sharepoint

I have inherited two environments one is an mvc environment with a custom hashed authentication writing to a sql table. The other is an on premise SharePoint 2013 environment that uses forms based authentication with a .Net membership database for authentication.

I would like to implement a single sign on between the two environments, where a user clicks a link from their user dashboard on the mvc environment and is directed to the sharepoint system and automatically authenticated on the .net membership database and logged in.

📷The biggest problem is that there are two different user databases and forms of authentication. How would you guys go about approaching this problem?