Want to rewrite hardcoded links in site to FQURL

I have a site which has hardcoded links that point to //Servername/sitename. There are many of them which is why we want to use URL rewrite. We want to have these links go through the module and append the FQ URL of the site but still take you to the links.

We have a rule setup to foward any //servername/sitename requests to redirect to the FQ URL but this does not affect these links. 

How can we write a rule to do this:

1. See the incoming request for //servername/site/LinkTothispage565
2. Grab the Link portion from url (LinkTothispage565)
3. Rewrite URL to http://FQURL.com/site
4. Append the Link back on the end http://FQURL.com/site/LinkTothispage565

Thanks all in advance.