The solution that eventually worked for me was to convert the database to ‘utf8mb4’. When MySQL talkes about ‘utf8’ they do not talk about UTF-8 despite the apparent similarities of the two names. That would have been too simple. ‘utf8’ is just 3*16 bits whereas UTF-8 fits into 4*16 bits.
After converting the database and making sure the phpMyAdmin interface is set to communicate in utf8mb4, it is time to change the file wp-config.php in the home directory of the wordpress installation so that the charset-variable takes “utf8mb4” instead of “utf8” and then it works.