I took more time to work with my moodlebox, read more artikels in this forum and read again the manual.
I was too concentrated to the information my Moodlebox gave me after the first boot (see picture above) on the screen. According to many threads obivously it doesn't matter that lsb, accesspoint and dnsmasq give this "FAILED" information.
My next fault was to try to connect via ethernet to the Box. As written (shame on me) it is in general not possible to connect to the Moodlebox by wire. After I took my Laptop, connected it to the Wlan of the Box and logged in, everything seems to run fine.
I think it should be possible to work to the Box via ethernet, because the usebility will raise.
Anyway, problem is SOLVED for me. I am really curious about how it works, because I see many benefits for my volunteer work to use it.
THX and merci beacoup again to @"Nicolas" and your team!