Hello Jeff Johnston,
You can print, but the Fax Service cannot.
This is the entire key to the problem. The Fax Service runs as the NETWORK SERVICE account by default. This account has almost no permissions on the network.
Your user account has permission to use FAX-PRINTER, but the NETWORK SERVICE account does not.
The error 0x00000BBB means ERROR_PRINTER_NOT_FOUND. This confirms that the service cannot see or authenticate to the network printer, even though you can.
You can try to do this solution:
The NETWORK SERVICE account authenticates on the network using the Fax Server's computer account (e.g., FAX-SERVER-NAME$). We can give that account permission to print.
Go to the Print Server (the computer that is sharing "FAX-PRINTER").
Open Print Management.
Right-click on your "FAX-PRINTER" and go to Properties.
Go to the Security tab.
Click "Add...".
Click "Object Types..." and make sure you check the box for "Computers". Click OK.
In the text box, type the name of your Fax Server (the computer, not the user) and click "Check Names". It should find it (e.g., FAX-SERVER-NAME$). Click OK.
Select the newly added computer account and give it the "Print" permission.
Click Apply/OK.
On your Fax Server, restart the "Fax" service.
Now, test by receiving a new fax. If this guide is helpful, please click "Accept Answer" so everyone in the community can benefit. If you need any other support, don't hesitate to tell me; I will always help you within my abilities.