Fanuc controller .... means you need a Fanuc post
2 axis post is for a basic turning only type machine
You have a C axis, but no Y
suggest you look for a 4-axis generic post with C axis...... you would then disable the Y axis component, so you don't get any unusable code.
- not sure about programming the transfer capabilities, but I think the generic post has it
Some mods may be required to suit your specific machine