Replace all URL's for my WordPress site using a different domain name?

Hi there and thanks for any help,

I’ll try to be as specific as possible with explaining this. The domain names used are only examples, so if you could use those example names in your answer that would be great. I’m having a very hard time wording exactly what I’m trying to do and because of that can’t find the answer via searching, so I’m posting it as this analogy:

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I work for a company that makes WordPress sites. We’ll call that company SuperMedia, and their main website is http://www.supermedia.com. SuperMedia wants to host their clients’ sites on their own server via subfolders. So in this case, we’ve created a client’s WordPress site in the directory http://supermedia.com/greatclient/

The issue is that our client has a domain name, http://www.friendlyclient.com, and we need to link this domain name to their site which we are hosting on our server, but we don’t want the urls to show “supermedia” at all.

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So in simplest terms, right now all of our page urls look like this:

http://supermedia.com/greatclient/about
http://supermedia.com/greatclient/our-services
http://supermedia.com/greatclient/gallery
(etc…)

But we want them all to say:

http://friendlyclient.com/about
http://friendlyclient.com/our-services
http://friendlyclient.com/gallery
(etc…)

but still display the information on http://supermedia.com/greatclient/about, http://supermedia.com/greatclient/our-services, http://supermedia.com/greatclient/gallery, and so on.

—–

Is there a simple, fairly fast way to do this for all the pages we’ve created, either using .htaccess or some kind of plugin? I don’t have a lot of back-end programming/database knowledge, so if it involves that could you provide me with some clearly laid-out steps on how I can achieve this?

Thanks so much in advance and if you need more clarification, please let me know.