make web browsers show up in a submenu of a main menu

[Felix Miata]

I've been looking at
https://specifications.freedesktop.org/menu-spec/latest/apas02.html
and
https://specifications.freedesktop.org/desktop-entry-spec/latest/ar01s05.html
and
https://specifications.freedesktop.org/desktop-entry-spec/desktop-entry-spec-latest.html
and elsewhere trying to figure out how to get my web browser menus to show up 
in Web Browser as a submenu of the main menu entry Internet when running any 
Linux distro other than openSUSE. This is how the KDE3 menu in openSUSE shows 
Konqueror, the rpm's Firefox menu, as well as the other Firefoxes and 
SeaMonkeys from Mozilla.org I have installed in /usr/local/ and created 
created .desktop files for in /usr/local/share/applications. The rpm's 
SeaMonkey, unfortunately, is showing up directly in the Internet menu, the 
reason for which I've yet to figure out.

When I use the same /usr/local/ tree to boot Mageia KDE4 or Fedora KDE5 or 
TDE in openSUSE, all my updated .desktop file entries are showing up directly 
in Internet. The only entries in the Web Browser submenu are old entries that 
generated Invalid key name: Exec[$e] errors until I deleted the files 
containing those keys.

I looked at openSUSE's /usr/share/desktop-directories and found .directory 
files for Internet and WebBrowser, but cannot unlock the magic that make them 
work. suse-internet.directory contains:
[Desktop Entry]
Encoding=UTF-8
Name=Internet
Icon=package_network

Type=Directory

and suse-internet-webbrowser.directory contains:
[Desktop Entry]
Encoding=UTF-8
Name=Web Browser
Icon=package_internet_webbrowser

Type=Directory

This is one of the browser .desktop files I made:
[Desktop Entry]
Categories=Network;WebBrowser;GTK;
Comment=Web Browser
Encoding=UTF-8
Exec=/usr/local/ff3/firefox -no-remote -P ff3
GenericName=Web Browser
Icon=firefox
MimeType=text/html;text/xml;application/xhtml+xml;application/vnd.mozilla.xul+xml;text/mml;application/x-xpinstall;x-scheme-handler/http;x-scheme-handler/https;x-scheme-handler/ftp;
Name=Firefox 3
StartupNotify=true
Terminal=false
Type=Application
X-KDE-SubstituteUID=false
X-KDE-Username=

How can I get the same menu nesting effect with other desktop environments 
that I get with KDE in openSUSE?
-- 
"The wise are known for their understanding, and pleasant
words are persuasive." Proverbs 16:21 (New Living Translation)

  Team OS/2 ** Reg. Linux User #211409 ** a11y rocks!

Felix Miata  ***  http://fm.no-ip.com/