There's no option to set a subject for that. The subject is user supplied. Best I can suggest is trying to override it using CB Auto Actions. The below should work.
Global
Triggers: onBeforeEmailUser
Type: Code
User: Automatic
Access: Everybody
Action
Method: PHP
Code:
Code:
$variables['var6'] = 'Inquiry from website: ' . $variables['var6'];
Parameters
Reference Variables: Variable 6
That should prefix the subject the user supplied with "Inquiry from website: ". For that trigger variable 6 is a reference variable and is the subject so it can be modified. Below are the other variables available to that trigger.
Code:
$_PLUGINS->trigger( 'onBeforeEmailUser', array( &$rowFrom, &$rowTo, 1, &$emailName, &$emailAddress, &$subject, &$message ) );