I have tested the other devices and the problem is also solved.
Thank you very much for the really quick solution!
Only some three weeks after that great solution WhatsApp changed the privacy settings for contacts. Now the setting for searching invisible contacts is removed and WhatsApp gets all contacts on the phone. For me it is a data privacy nightmare, because I do store contacts from people for I do not want to share their number with WhatsApp.
Does someone has an idea how to deal with that problem?