Hi, thanks for your answer.
I tried to duplicate the issue on my local pc. And as you said, there it worked fine.
Then I figured out, that the issue only occures, when I activate the plugin for the whole network.
But when I activate the plugin for each part of my multisite step by step, It seems to work like a charme.
So, as I said, only when I activate the plugin for the whole network in the network-managemend, the issue occours