There are a few extra steps required when attempting to use a Portsmith ethernet adapter with a Windows Mobile device:
(If you cannot connect your device to your PC with ActiveSync/WMDC, you can connect your device to the internet and follow the steps to on your device, or email the mentioned .zip file to your device.)
Go to https://www.portsmith.com/product-category/cradles/ and select the cradle for the device you are using."
In the "Supported Devices" table find the device you are using and click the "SMSC Driver" link to download the correct application.
Inside the .zip file that was downloaded is a .CAB file that needs to be moved over to your device.
Open the .CAB file on your device to ensure that it works properly. The application should now be on your device.
You can now follow the normal steps for using the adapter to ensure that your network cable is plugged into your network (and NOT into your PC).
If you ever need to use ActiveSync/WMDC again you will need to enable it in the Portsmith application and you will be able to use them the next time you connect.
You may also find this document from Portsmith helpful for a visual guide.
For further reference on how to configure the adapter hardware, below is a reference picture of the adapter being used with a cradled Zebra MC67.