WordPress site through proxy domain

Trying to proxy the content of a wordpress site sat on one domain through another domain but the engineers are telling us there is a redirect that breaks the proxy. They have told us the way it is usually done is to make the fully qualified URLs that WordPress requires match the masking URL so in this case all the FQDN in the site should be http://www.themaskingdomain.com

We’re stuck, how would we go about doing that?

Thanks