I’ve checked my other plugins and found an option there, which denied access to admin dashboard accept for admins. I had to uncheck and check this option again there. I think it has overwritten the “view admin dashboard” and “read” permission in user role editor. now it works fine. I granted access to the named two permissions and the new user can access the dashboard.
Sometimes it is too deifficult so keep an overview of all options in all plugins ^^
But thanks for your fast response @Vladimir and HAPPY NEW YEAR 😉