cookie is not there for private window shortcut without main browser is running

[rayfeng10203]

Hi, I created a firefox private window shortcut as C:\Program Files\Mozilla Firefox\firefox.exe" -private-window in desktop.
I found I can close this shortcut and reopen with cookie saved only if the main firefox is running, otherwise, any cookie saved in private window won't take effect after close and reopen the shortcut.

Can this firefox private window shortcut save and restore cookie without main browser ?

Thanks