Simple to remove and Moen aren't often in the same sentence! If you're lucky, maybe. In theory, yes, it should come out, but in practice, just search through threads here, you'll find lots of people cussing the things. At that age, you'll probably need the pro version (metal) removal tool as the plastic one will probably break. Moen will probably send you a new cartridge if you call them.
But, I'm not really familiar, and aren't sure if it is Moen.