SOLVED:

The problem was the path delimiter and the root disc name.

Replacing : with forward slash (/) resolved the problem.

The corrected code snippet is:
   
   TmpPath = "/Users/" & TheUser & "/Library/Group Containers/UBF8T346G9.Office/User Content.localized/Templates.localized/ERI Templates/"
   TmpName = "NumberedHeadings.dot"
Also the explicit naming of the disc the template is located on is also dropped. Replacing "Macintosh HD" with "/" was also needed.

I haven't seen this change documented at any of the VB MS sites.