Advanced messages (or Enhanced messaging) use a new messaging technology called RCS. RCS messages are currently not supported by our app, and the reason is that these messages are not stored in the SMS/MMS database we have access to. Instead, these messages are stored in a database that’s not accessible to us, at least not yet (or any third party apps). We don’t know yet when our app will support this because RCS is still under development and the companies behind RCS have not yet released an API for developers to access these messages. This is one of our top priorities and we are following the development of RCS closely. Please visit https://jibe.google.com for more information about RCS.
You can check if you are using RCS in your messaging app by long pressing on a message (that was not backed up) and select Show Details, if it says “Advanced Message” or “Chat” then this is an advanced message (called RCS), it’s not an SMS or MMS message. At this stage, SMS Backup & Restore does not have access to RCS messages. If that is the case and you are not using any features offered by Advanced/Enhanced messaging, then you can disable it from your messaging app settings.
This only affects outgoing/sent messages and incoming/received messages still get backed up correctly. Any messages sent after changing the setting will then get backed up by the app.