If the phone switches networks, then it would have to create a new connection. The router can behave the way you describe only by having a server listen on port 80 (HTTP) and then proxying data back and forward to a different session over HTTPS. A simple configuration issue cannot produce the necessary servers and proxying behavior for your scenario to be valid. There is the [SSLStrip][1] attack that is similar to your description but it involves many more steps. [1]: http://www.thoughtcrime.org/software/sslstrip/