Hello Ernest,
thanks for your answers!
1) The grouping seems to work!
2) I also added your code to functions.php, unfortunately it does not seem to have any effect. You can check the results again on the search page. However I also do not think this solution is suitable for us. We do not need any info from the page or post but directly from the pdf. Is there any chance to get some additional info out of the pdf? For example the page number on which the search term was found? Or e.g. 50 characters before and after the search term? It is just about making it easier for the user to find the search term when opening the pdf file.
Thanks!
Georg