I have just reported a bug with the telegram-desktop package, along with a potential fix, but I am wondering whether this is MATE specific and the bug isn't seen with the Gnome desktop. During my investigation I've also noted that the different menu options for the panels display a different selection of applications based on the same set of .desktop files. My assumption is that the Brisk Menu deliberately ignores all applications that run from a terminal (Mutt shows in the Main MATE Menu and Advance MATE Menu, but not in Brisk).
The issue I've found with Telegram is that the Mime line in the .desktop file stopped it showing in any of the menus:
Does anyone know if this is likely to be due to an unknown Mime type or the syntax. The syntax looks good to me, but there is nothing for tg in /etc/mime.types. It seems better to fix this rather than simply remove the line. It is also more likely to be accepted by the package maintainer!
What I can't test at the moment is whether Telegram shows in the Gnome menus that will be used in the standard Ubuntu install.