“All that said, there is a place where NoNonsense Forum sort of simulates the existence of logged in users. The little sign in link in the footer of this very page. When you click it, your web browser will ask you for your username and password. (Important: your browser asks you, not the website!) When you enter your login there, your browser will send it to every page every time.”

Understood, so now I manage to add the menu for Sign-in user. in themes/greyscale/index.html.

and add the new menu ID

//is the user already signed-in?
))->remove (AUTH_HTTP
//don’t need the usual name / password fields and the deafult message for anonymous users
? '#nnf_name, #nnf_pass, #nnf_email, #nnf_error-none'
//user is not signed in, remove the "you are signed in as:" field and the message for signed in users
: '#nnf_name-http, #nnf_error-none-http , #new_menu '

So, is it correct ?

“Using the theming system, you should be able to add an extra menu to the forum and then add a little bit of DOM templating [3] to your theme’s theme.php file where you use the `AUTH_HTTP` constant in the same way as the forum is doing in index.php.”

I will take deeper on DOM templating.