Fully cooked pork shoulder but not cooked enough where it shreds. I want to turn into carnitas.

I'm not sure what you consider carnitas but I usually roast the shoulder at 300 for 6ish hours, pull it, reserve the fat and then either pan fry it in its fat or toss the shredded meat with the fat and put it in a super hot oven for a few minutes to crisp it up....anyway, as most have already said, "fall apart tender" has absolutely nothing to do with temperatures, so just be patient and check it with a fork every now and then. It will eventually shred.

If you don't want to wait 6 hours, 325 at 3.5 - 4 hours also works, but the slower the roast, the more silky the texture, I find. Adding moisture will not keep the meat moist.

cook it covered with a small amount of cooking liquid for an hour or two, checking every so often, at 250. it just needs more cooking. once it is shreddable, continue on to carnitas.

If it's not falling apart it really isn't done. You have to cook it low and long enough so all of the connective tissues melts away. Maybe throw it in a slow cooker till it gets nice a soft. Carnitas are usually slow cooked in oil or lard. Maybe a slow braise may help. add some beer for moisture.

You have to cook pork to 195 F for it to shred. It will be fully cooked at the lower temp of 165.