Answer: The plant is most likely suffering transplant stress. Often, transplanting will also leave behind a good proportion of roots and this will be compensated for by an effort to reduce water loss through the top portion of the plant -- or wilting.
Although wilting can be a sign of underwatering it can also be a sign of overwatering. This plant does not tolerate overly wet soil, so you need to be careful about how you water it.
Your goal is to keep the soil slightly moist but not sopping wet or saturated. You will need to dig down with your finger and see if and when you need to water again. A deeper watering will encourage deeeper roots and is better than a more frequent light sprinkling. You might want to water, wait several hours or overnight, then dig down and see how effective your watering was -- it can be surprising. Using several inches of organic mulch will help to keep the soil more evenly moist.
At this point, keep the soil evenly moist and be patient. Next spring, you may find somewhat more winter damage than usual, but just trim away any dead branches in early spring. The plant blooms on new growth of the season so, assuming you were able to take a good proportion of its root system when you dug it up, the plant should recover from the move during the coming year.
Good luck with your rose of Sharon.
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