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The best time for transplanting peonies, rhododendrons and azaleas is in the Fall when the plants begin their dormant cycle and they can be safely dug and replanted. When transplanting, be sure to dig a large root ball, getting as much of the root system as possible, and try to get the plant back into the soil quickly, so the roots do not dry out from air exposure. Always dig the new planting hole considerably larger than the root ball of the plant you are transplanting. This will insure that the new roots will have rich soil to become established in.
I Found this to be a good tip but you may also want to add about the need to keep rootball well watered throughout the transplanting period and after planting care ie regular watering if dry mulching to keep plant moiust and use of fertiliser to suit plant.