Fiddler and FiddlerCore are proxy servers, which means that they accept requests from clients and send the traffic to wherever it was originally destined.
You could, in principle do several things related to your request:
1. You could run Fiddler or FiddlerCore as a Reverse Proxy
on server, such that Fiddler would collect all of the inbound traffic before forwarding it on to whatever web application it is running as a reverse proxy for. Your web application could provide a way for the client to view the traffic that they had sent.
This approach would allow you to collect and display traffic from clients without reconfiguring them, but it would only show traffic sent to your specific server.
2. You could run Fiddler or FiddlerCore on a server and have one or more clients manually configure their proxy settings to point to that Fiddler instance. A HTML interface you write could provide a way for the client to view the traffic that they had sent.
This approach would allow you to collect and display traffic from clients sent to any server, but it requires manually reconfiguring the client.
There is no option #3, wherein the Fiddler instance on a server could somehow act as a proxy for arbitrary sites without reconfiguring the client.
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