Hi schtumpy,
Most modern software (poser included) makes changes to the registry of the system it is installed on. So, you need to install Poser on the new PC. Then you can copy the Runtime folder (or folders) from the old PC over the Runtime folder on your new PC and you will get all of your purchased and free content back without installing it all again. Just make sure that everything you copy over is at the same path.
The networking is quite straightforward since you can set up a simple drive or folder share (for yourself) on the old PC. [e.g. Use a My Computer browser and Right click on the Poser installed drive on the old PC and select Sharing and Security from the menu. Add a network share and give it a name you will recognise]. Then use the new PC network neighbourhood browser to find your old PC and browse into the shared drive.
It is not such a good idea to use the existing SharedDocs folder as you would have to copy everything into this folder on the old PC and then copy everything out again on the new PC.
HTH,
Jovial.