Just connect the audio to the line input of the sound card, then you could use an MP3 encoder like Simplecast, and run a server like Icecast on the scanners PC. Then connect to the IP of scanners PC directly on the LAN and listen with windows media player. I've done this to monitor my stream locally on the LAN, but maybe there is an easier way for your LAN only use, not sure.
Another way I listen to the scanner from another part of the house is with bluetooth like this...
