Are you using Delete browsing, search and download history on Firefox to clear the cookies?
You can try to exclude the cookies to see if that helps.

You can let all cookies expire when you close Firefox to remove unwanted cookies and keep the ones with an allow exception.

• Tools > Options > Privacy > Cookies: "Keep until": "I close Firefox"

Extras > Einstellungen > Datenschutz > Firefox wird eine Chronik: nach benutzerdefinierten Einstellungen anlegen
"Cookies akzeptieren" : Behalten bis: Firefox geschlossen wird

Thanks for Your quick answer, cor-el ! I´m sorry, but the reason for the behaviour of Firefox didn´t depend on the Cookies...

AND YES= My Laptop "speaks German" ! Do you know any other installation, that I could try to change, that could make Firefox shut down faster?

With many thanks in advance from Finland !