How to get persistent (that is listed in notification list activated from system tray) notifications from Thunderbird about new emails arrived? I use GNotify.
In fact, I have tried just to send something with 'notify-send', and I see popup message, but nothing is accumulated into notifications list.

Persistent notifications (those stored in history) are only those that are marked as persistent by the application that is creating them.

If you want to store something with notify-send, you need to add "-t 0".

Great, thanks for the clarification!