I tried to find out why this was happening. It was because of a "new" message type called RCS: https://en.wikipedia.org/wiki/Rich_Communication_Services
I didn't want to reinvent the wheel - there are already enough backup/restore apps for SMS and MMS. Instead I just wanted to make an app that was able to export the RCS messages, too. Preferably it should be a format that SMS BR could then import.