Autocomplete uses the local address books such as Personal Address Book and Collected Addresses by default, but it may appear to not work if the Email field for contacts is empty (due to faulty address book import), or if there is an incompatible add-on (such as older versions of MoreFunctionsForAddressBook.

I want to simply check if autocomplete is enabled. But I need to know which German terms are used for Tools/Options/Composition/Addressing. The simple translation does not help, but for sure screen shots of the English version for the 4 steps of Tools/Options/Composition/Addressing will help.

See the pictures. Press the Alt key if the Menu Bar is hidden, to see the Tools menu.

now I am sure the autocomplete is ON but Thunderbird does not do it. What should be the reason? I have no idea.

See my first reply: open Address Book and double-click a contact. Is there a valid entry in the Email box? If all your contacts have addresses in the Email box, select Help/Restart with Add-ons Disabled and see if autocomplete works.

I didn't do nothing; but by magic now it works