Hello mate,
I think you are looking for single sign on functionality. We use CAS to implement SSO in our University but I think this might be a bit of an overkill if you are planning to keep it simple.
You could try form emulation, this would be the fastest way to achieve the desired functionality but this is very unreliable and fraught with security holes. The next best thing would be a custom auth plugin. Obviously this requires a little bit more work, but I believe this is the recommended way of achieving the functionality you want. Have a look here http://docs.moodle.org/dev/Authentication_plugins
Before we implemented CAS, we wrote a custom plugin called GateKeeper which allowed single sign on from a particular set of applications.
Regards
Ravi Alamuri