I can confirm this problem too. I changed (System->Preferences->Main Menu) the icon of Thunderbird and this new icon is used from now on in the "internet" section. But when I add Thunderbird to my favorites, the old icon is used in the "favorites" section. However, in the "internet" section the new icon is still used.
I can confirm this problem too. I changed (System- >Preferences- >Main Menu) the icon of Thunderbird and this new icon is used from now on in the "internet" section. But when I add Thunderbird to my favorites, the old icon is used in the "favorites" section. However, in the "internet" section the new icon is still used.