Convert the url of a DirectAction

Hello,
I made a website for which you go threw the connections window by a  
DirectAction. The problem is that I must now convert this site into a  
secured site. The url have been already send to the customer that's  
why I would like to convert a HTTP url that I receive to a HTTPS url.  
Like that the custumers will be able to get connected without any  
problems and they won't see any difference. Is there anyone who had a  
similar problem and have a solution to this problem?

Thank you,

Simon