I would need our webpage to automatically login user when he clicks on a button.
So I have logged user in our webpage. Logged user will have some form leading to roundcube webmail. You have to tell me how to craft such form that will allow user to be logged automatically without need of entering password. We DO NOT store plain passwords so maybe you have to use roundcube external auth module and only compare usernames. (maybe this can help? [url removed, login to view])
You have to tweak roundcube (latest version) to allow such login.
Please think about (and implement) also some security,