Take a report on the main investigation or not?

In the end, the employee said that I didn’t have to carry the wipe along with the papers. The data of the passed examination are reported to the KBA every evening and they then report to the registration offices. Therefore, I no longer have to be able to present the report with a police check, because it can be checked online. Now, I have never had to show the report at two or three checks in the last ten years. However, would I like to know a) whether I can actually leave it at home? b) since when is that (can I also leave a report from 2024 at home)? c) whether this also applies to the sale, i.e. the re-registration to a new holder? My registration office writes on its side that it is necessary to provide proof of the last main examination.