Okay, it turns out that I was missing a tiny little number in the add_filter
command. The line:
add_filter( 'the_content', array( &$this, 'after_content' ));
should be:
add_filter( 'the_content', array( &$this, 'after_content' ), 12);
And now all works. The array is accessible inside the filter-function. This number is a priority variable: https://developer.wordpress.org/reference/functions/add_filter/, but if anyone will add a comment on the usefulness of it, please do so.