Browser developer mode (press F12 to enable) shows: Blocked loading mixed active content - tries to access machine name of GroupShare Web Server on HTTP instead of public URL
 

Manually edit the file C:\Program Files (x86)\SDL\SDL Server\Web\resources\config.js to reflect the correct GroupShare URL / External Server Address that was entered on the GroupShare App Server - in the GroupShare Console

The file C:\Program Files (x86)\SDL\SDL Server\Web\resources\config.js from the GroupShare Web Server does not contain the public URL that was configured in the GroupShare Console. This is a confusing situation because the GroupShare App server also has the GroupShare Web role installed (and not used) so when changes are done in the GroupShare Console to the External Server Address - there is no error shown. Which leads the user in thinking that everything was updated correctly when in fact it was not. See the behavior when the GroupShare Web role is not installed on the GroupShare Application Server (not recommended setup):

Error in GroupShare Console in split-scenario - An unknown error occurred. Please restart the application. Details: Could not find a part of the path