Interesting. Normally, when one has access to external drives, the Desktop is automatically adjusted as well. Please go into your System Preferences, and select the Security and Privacy tab. Then scroll down on the right side until you get to the Files and Folders option, and be sure that the Desktop is checked. If it isn't, click on the lock in the bottom left corner, provide your administrator password, and then check any of the boxes that are not checked, as shown in the screenshot below.