Once the user is logged in you could have a OnLayoutEnter script trigger on the layoutthat gets your login details and passes them as a variable to your Web Viewer.
Does the URL you are using allow username & passwords to be passed through it?
did you know any web mail just open from filemaker passing credential. please let me know
I think, we need API or URL which web mail using they are provide authenticate URL, I dnot know any other option