I finally succeeded, at eight or ten attempts. Hurray!
I tried three other SD cards.
I tried both the server and desktop version of the installation.
I tried directly attached keyboard and monitor as well as a remote shell.
Helped probably one of two things: The power from a laptop instead of an adapter (5V/2.5A) or set the correct time and date before start the upgrade.
dubraro got a reaction from Igor in Running apt-get dist-upgrade installs the new kernel but takes the Orange Pi PC a really long time