Um...
"That can't be done."
"Yes, I know, but can it be done?"
A resource isn't something that can be written down - it can't be converted into a string. And because it can't be converted into a string, it can't be stored in the session data.
A resource that contains a Telnet connection can't be written down because some of it is on the other server. If you could get the other server to store everything relevant it has to the connection, and if you could get both it and your machine to record a common token so that when (if) your machine wants to continue the connection both computers can recover all their state, then you might be on to something.
Another possibility is if you had an entirely separate program on your computer continually running and keeping the Telnet connection open. Then your script would talk to this program and this program would talk to the Telnet server.