FreePBX to SMS (via bluetooth mobile phone)

Likely, but it would be custom, and I couldn’t find any material either. You would need to see how the SMS data is coming in and do something with it once you have it. Again, you’d likely have to develop this yourself or pay someone to do it for you.

There is this tool, which could give you a user interface, if you adapt it, but again it does not support what you are wanting to do out of the box.

New open source SMS Connector module - FreePBX / Development - FreePBX Community Forums