forward php references to another subdomain?

I have a client that has a web API sitting on www.client.com/api/api.php with old versions of mySQL on the back end, thereby making it difficult to relocate in the first place.
They redesigned their website and want to change the IP address of the WWW subdomain to their new hosting provider, HOWEVER doing so will break the existing api that their customers are using because of the file path using WWW. They are required by contract to give their customers 1 year notice before change the path of their APIs. So the question is can you have (post hosting change) www.client.com/api/api.php transparently forward to the old hosting server where the api subdomain will be renamed to something like app.client.com/api/api.php. They are not using HTTPS for the api.