Symmons shower isn't producing hot water
I does sound like your cartridge has gone.
It's hard to see from the photo, but It looks like this is your valve:

It looks like you can actually just replace the spindle:

You should just be able to unscrew it from the main body if you get an adjustable wrench on the flats on the front of the threaded section just behind the splined part.
Notes:

Don't forget to shut off both supplies up-stream!
Even with the water shut off, you will likely still get some coming out when you remove the cartridge. I tuck a sheet of plastic around the bottom, and as far behind as I can go to try and catch this, so it doesn't go into the wall cavity.