I've divided and moved artichokes without any problems, I mark the plants when they die down and then either when dormant or normally because I'm a lazy person when I see them start to sprout in the spring. I cut off the outside buds with a sharp spade angled to cut under the plant so you get a bit of
root with the sucker. I don't treat them I just move them to where they are going to live, I don't do anything else, but of
course if you live somewhere
dryer than me watering would probably be a good idea.