add www to a https host

That's actually very simple to do. Apply this iRule to their Virtual server and they should be all set.

 when HTTP_REQUEST {  
   if { !([string tolower [HTTP::host]] starts_with "www.") } {  
     HTTP::redirect http://www.[HTTP::host][HTTP::uri]"  
   }  
 }

This will essentially check the value of the Host header and if it doesn't start with "www." it will issue a HTTP redirect to the client browser with www. added to the beginning of the URI.

If the customer doesn't want to do this for all requests, but only for the single domain "customer.com", you could do something like this:

 when HTTP_REQUEST {  
   if { [string tolower [HTTP::host]] eq "customer.com" } {  
     HTTP::redirect "http://www.customer.com[HTTP::uri]"  
   }  
 }

Hope this helps...

-Joe