Processes in Microsoft 365 for setting up Office apps, redeeming product keys, and activating licenses.
I had to downgrade from Office 365 with 2016 apps first release to Office 365 2013 because Office 2016 was still buggy and was only meant for testing.
Anyway, I also experienced this problem to the extent that after a reboot my Outlook 2013 control panel icon went missing and the Outlook 2016 icon was presenting a file missing error when I clicked the mail icon.
Solution for Windows x64:
> Navigate to the registry key HKEY_LOCAL_MACHINE\SOFTWARE\Classes\Wow6432Node\CLSID\
> Run find, the search for the name of the control panel icon you want to remove/fix, in my
case I searched for "Mail (Microsoft Outlook 2016)"
> It will find the string inside the CLSID subkey. Delete the relevant subkey, for example see attached screenshot, in my case I had to delete {A0D4CD32-5D5D-4f72-BAAA-767A7AD6BAC5}.
> After opening the control panel, the correct Mail icon appeared and the registry key regenerated itself with correct values.