Establishing a split-terminated communication connection through a stateful firewall, with network transparency

A method and apparatus are provided for establishing a split-terminated client-server communication connection through a stateful firewall, with network transparency. In an environment in which a pair of network intermediaries is employed to optimize client-server communications, a first intermediary intercepts a client request for a new connection. The first intermediary probes the network for a counterpart near the server, and opens an optimized communication session with a second intermediary that responds affirmatively. Some or all client-server communications that transit the intermediaries' session are accelerated or otherwise optimized. The first intermediary's probe uses the client's source address, but a different port number, while the optimized intermediary session is opened using the client's source address and source port. Therefore, a network monitoring tool can monitor the end-to-end connection, and the stateful firewall will not reject the optimized session.