You don't. You keep the socket open in the server and give the client a session id (see CGI::Session) using which you can find the appropriate socket back in your server program.

Thank you for being patient, but sorry, I dont get it (not my best day, obviously:)). Are you suggesting that I serialize the socket and store it as a session scalar and deserialize it back in the next pass of the same session? I doubt that you can do it with sockets.

Yes. You cannot serialize sockets. So you need a persistent program on your server that keeps the socket open. That persistent program gives the client ("web browser") a token ("a session id", "a cookie") that associates the socket with the client. When some client connects again to your server process and presents the appropriate token, you know which connection to reuse.