Hmm, now PPP is the hot topic. But the cellular module should be capable of sending SMS.
Its like the documentation is the driver-code itself. I think lots of people would like a few simple examples for the basic functionality in the module as well.
One thing to keep in mind. As you only have 1 serial port and the driver is not using the MUX protocol, is that when you are connected to PPP, you cannot receive SMS or send them. The module will receive them internally but won’t be able to advise you of the arrival.
If you need both at the same time, you need to disconnect the PPP and then check for SMS and then re-connect PPP again.
USB modems are pretty good for this as they have 2 separate channels, 1 for AT commands which you can do the SMS checking with and the second one for PPP.