First of all, you would need to create a "Process Builder" on the "Incoming SMS" object.


image


In the condition diamond, you can put the field named as "Case" Isn't Empty and any other criteria in your mind!

image


In the actions, you can choose to "Record Update" and set the Case.Stage field value to the one you wish to change it to.

image


Details of the Action: 

image


P.S.: The stages have been chosen for your reference, they are the stages set to Case objects in my org.