Whatever you do, don't listen to anyone who tells you to prune the top of the plant to compensate for root loss. If ANY plant is to have the best chance of surviving and thriving after being transplanted from the ground, it will require all of the energy producing leaves. Root development relies on those leaves.

Heavy top pruning will result in an automatic response by the plant to grow....more leaves! Since plants can't send their valuable carbon resources to two completely different locations at once, the leaves will be replaced first. Then the plant will begin to establish a new root system.

I'll attach a pretty good fact sheet to see what you think. If you have more questions, please do not hesitate to ask.

Here is a link that might be useful: Transplanting established plants

Bill, their shallow rooting habit makes azaleas one of the easier shrubs to move - not that some weight won't be involved with plants that size and you may well need another pair of strong arms. If you haven't transplanted azaleas, some guidelines:

You will find a surface network of roots (that you can expect to extend as far as the widest stems) and just a few larger anchoring roots. It's safe to take a smaller rootball, if possible, aim for a rootball equal in diameter to approx 2/3s the plants height - or as close as you can come to that.

With a little care, you can usually move successfully any time the ground is not frozen or the plants are not in active growth. The period of active growth is immediately after blooming.

Drag them on a tarp or sheet of cardboard rather than pick them up by the stems when moving one of any size, or the weight of rootball and dirt will damage roots.

Prepare the new site before removing from the old, be careful not to plant them any deeper than they were originally growing. If the new site has been spaded overall, allow for some settling, a little high is better than too deep.

Mulch the rootzone will after replanting, pay attention to water the first year after moving.

And ditto Rhizo's suggestion not to prune to reduce the size.

"Mulch the rootzone will after replanting". No, mulch it well, as in thoroughly. Sigh. Why don't I proof read, then submit, not the other way around.

You can make moving a large azalea much easier if you follow the recommendations on the Clemson extension sheet that rhizo posted:

"Roots of shrubs normally grow well beyond the soil volume that can be moved. To keep most of the roots within a small area, root prune in the spring or fall before transplanting. Plants to be moved in the fall (October or November) should be root pruned in March, and those to be moved in spring (March) should be root pruned in October. Root prune only after leaves have fallen from deciduous plants in fall or before bud break in the spring. Plants may be damaged severely if done at other times. Roots within the pruned area grow many branches and form a strong root system within a confined area. If not root pruned, the plant may die from transplant shock because of root loss."

Following this procedure, you create a dense root ball that is smaller than what you would need if you just went out and started moving without root pruning. Naturally, the roots are very spread out and usually go beyond the drip line of the plant. You reduce the weight of the root ball by at least 50% by root pruning. To do this, root prune at 70% of the distance out from the stem to the drip line. To root prune just stick a spade into the ground in a circular line around the plant. Since the roots are shallow, a normal spade depth into the ground will cut most roots that extend beyond that line.

You need to wait the approximately 6 months after root pruning to give the new fine roots time to grow within the new defined circle where you root pruned. The new roots will be much more fibrous and hence, more efficient, but since they encompass a smaller area, watering is more critical

Here is a link that might be useful: Clemson Extension Fact Sheet

I can't add anything to the moving part, but I do want to mention that it should do very well after it is moved. I know that when I discard the remains from pruning my azaleas, the following spring I have new azaleas growing without any work. In other words they seem very resilient, to say the least. :)

The advice found on Clemson sheet and rhodyman's post certainly will not hurt, but the process of root pruning is, in my experience, unnecessary for rhododendrons and azaleas. The Clemson advice should be followed for large established shrubs of other types, but rhododendrons have shallow and densely fibrous root systems which almost never extend beyond the drip line of the plants. Cutting in a circle around the root mass with a sharp spade, prying upward as you go, sliding the root mass onto a tarp and then dragging it to its new location is all that's needed as long as it's kept well watered and mulched in the new location. Even if some of the roots are lost, the plants make a quick recovery assuming the new site has been well prepared.