Telegram 2.1.7 launcher icon not showing up ubuntu 20.04

Looks like the desktop file is not executable.

Open a terminal, and run the command

chmod +x .local/share/applications/telegramdesktop.desktop

You might have to logout and login for it to show up in the menu.

If it does not work, replace the contents of the file .local/share/applications/telegramdesktop.desktop (using the command gedit .local/share/applications/telegramdesktop.desktop) with the following.

[Desktop Entry]
Version=1.0
Name=Telegram Desktop
Comment=Official desktop version of Telegram messaging app
TryExec=telegram-desktop
Exec=telegram-desktop -- %u
Icon=telegram
Terminal=false
StartupWMClass=TelegramDesktop
Type=Application
Categories=Chat;Network;InstantMessaging;Qt;
MimeType=x-scheme-handler/tg;
Keywords=tg;chat;im;messaging;messenger;sms;tdesktop;
X-GNOME-UsesNotifications=true

You might have to run chmod +x .local/share/applications/telegramdesktop.desktop once again.