I don't get why you would even need a B.html to store the information and then insert into C.html with a iframe.
First up you can parse PHP in a html page with a little code in your htaccess file
then all you need to do is create a user database that once the log in it redirects them to c.html and you do this.
RemoveHandler .html .htm
AddType application/x-httpd-php .php .htm .html
Where you need the users info to be inserted into the page.
This LINK will explain how to create the user database and login script.
Then you need to create the userinfo.php and pull the info you want from the database.
Tiz simple.. ... really..