Thank you very much for your quick answers.
I solved the problem by installing
sudo ./linux-brprinter-installer-2.2.1-1
I went through all possible tutorials several times, but nothing helped but the installation of this Brother support entity.
This solved the problem.
I suspect a possible USB port corruption or lack of support for USB 3.0, because the scanner came to life when I passed it to another USB 2.0 port on my HPG255 laptop.
I will add that Ubuntu was upgraded from an older version on which drivers were already installed with a working scanner (on this port) and a working printer.