Unscrew the cap. Put the screw back into the stem. Then grab it with a pair of pliers, push the stem in and they YANK it out hard and quick. You will probably have to repeat the "push/pull" a few times but it will come out.
People are paying me for my time, so I do NOT soak anything in vinegar or anything else. Remove the cap, pull the cartridge, put in the new one, and make out the bill.