Thanks Kemical
OK-- I think I have figured it out.
It appears to me that the article ref above is not entirely accurate.
Also confusing is this
===============================================================
3. In Windows Explorer, navigate to the 
hidden system folder below. (See  screenshot below)
 
NOTE: You can  also open the Start Menu and right click on All Programs,click  on Open All Users, and open the Programs folder to get to  this location below as well.
C:\ProgramData\Microsoft\Windows\Start  Menu\Programs
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The NOTE says to open this --  C:\Users\All Users\Microsoft\Windows\Start Menu\Programs -- which is clearly not the same as the referenced path.
The ADMINISTRATIVE TOOLS is not actually STORED in
C:\ProgramData\Microsoft\Windows\Start Menu\Programs\Administrative  Tools
That location is dynamic. IE, when a user logs on the contents are replaced with the contents of
C:\Users\All Users\Microsoft\Windows\Start Menu\Programs\Administrative Tools
In fact, the entire Start Menu folder there is dynamic and depends on the user logged on.
It is actually a sum of ALL USERS and the logged in USER profile.
The issue with ADMINISTRATIVE TOOLS is that the entry under ALL PROGRAMS is a list of items in BOTH
    ALL USERS and USER PROFILE   (C:\Users\xxxxxxxx\AppData\Roaming\Microsoft\Windows\Start Menu\Programs\Administrative Tools)
What appears on the Start Menu right pane is ONLY what is in ALL USERS.
Since I did not want all users to access the admin tools, I moved them all over to my profile
therefore nothing appeared on the Start Menu -- Administration Tools ---
THEREFORE, if one has LOST the admin tools in the start menu it is because they have removed the folder
C:\Users\All Users\Microsoft\Windows\Start Menu\Programs\Administrative  Tools
which needs to be replaced
If one does not want the admin tools on the start menu then they must all be moved to the user profile and/or just tick the right choice in folder options since it will be empty.
I would not have done it quite that way.