web service redirect responce, can it be done?

OK, so here is the task at hand. We just signed a client that needs us to create a web service that does an action, that our system normally does on our internal data, on their supplied data, but the responce doesn't go back to them it goes back to a 3rd party. Our CTO said it could be done when they sold the client, but now that I am about to write it I am having trouble figuring out what direction to go with.

I was orignially going to do a simple .asmx service since all we are dooing is getting set data and running an already coded process on it and send it back, but that changed when we heard we are not sending it back to the requester. We are at the inital develpoment stage, although our existing web apps are c# asp.net (4.0) apps, so I want stay within the framework or maybe go to WCF (although I have never used it) if that is a better solution. Our CTO says if we register a certificate the we can open a secure socet and push the data to the 3rd party, but I am really unsure how that works in terms of a web service response.

Here is a quick data flow:

[New client] -------- > [our applications new API I am suposed to build] ---------> [Clients Vender 2 who ill do something else with the response data] with no other responces back to the client that initated the request...

I have done a few dozen web services in the past (older .net2.0 .asmx SOAP style, about 3-4 years ago) so when this project came up our CTO chose me to design and implement it since I had done the web services in the past, but it's soo different I am unsure where to start. Our platform is newer then when I last did a web service, there are newer frameworks I could use (but never had before), and I am unsure how to even push the data that is normally returned to the requester to the 3rd party. Thanks for the feedback...