I have a situation where some but not all of my target groups that exist in the native WSUS console and show under "Computer and Groups" in the Patch Manager console do not show up when I select "Approve" for Third Party Updates.
The list of WSUS Target Groups is captured and cached from the Server Node of the Patch Manager console. Normally, when you create WSUS Target Groups from the PM console, an automatic refresh is generated; but if you have created Target Groups from the WSUS console, they will not be. But any groups that appear in the "Computers and Groups" node of the Patch Manager console definitely should also appear in the Approval Dialog. Try running a "Refresh Update Server" from the WSUS node of the PM console and see if that resolves the issue.
If not, please open a ticket with Customer Support so we can take a deeper look at what might be happening.