I think the easiest way would be for your folks to take a shuttle from the Munich airport to Ostbahnhof (~30 minutes) and then transfering onto a westbound train line that will take them to Stuttgart (~2.5 hours).
Here's a link to more info
From Stuttgart's main station they can then transfer onto the S-Bahn S2 or S3 to the Stuttgart airport (~30 minutes).
Here's a link to more info
If language is a barrier you may want to call ahead and get more assistance from some travel professionals there to maybe get tickets now and so you don't need to worry about getting lost, getting on the wrong train, the wrong bus, etc. But that's how I would do it. Good luck!