There isn't any real reason to prune, they have a shallow rooting habit that makes them somewhat easy to transplant.

You can assume the roots extend out as far as the widest branches, but taking a smaller rootball is generally safe. Aim for a rootball equal in diameter of two thirds the plants height. Rather than lift by the branches and let the weight of the soil break roots, drag it on a tarp or sheet of cardboard to its new site.

They can be safely moved any time they are not in active growth (right after bloom) or the ground is not frozen. If your summers are hot and winters quite cold (harsher climates than my own), best results are usually obtained when you observe the same timing as is recommended for new plantings in your area.

Be care not to plant it any deeper than it was originally growing, mulch and keep watered.

Sure. Be sure to root prune also. When transplanting a large plant several steps should be followed.

* First, it is best to stimulate a tight root ball by root pruning the plants to be moved before moving. This is accomplished by cutting a circle around the plant stem with a shovel to cut off roots that extend beyond this point. This radius is usually about half way to the drip line.

* Second, it is best to move when the plant is dormant and not stressed. This would be in the spring and fall when the plant is still dormant but the soil is not frozen. Moving in the fall before the ground freezes is preferable if you don't have a problem with frost heaving. Sometimes winter freezing and thawing cycles can actually lift a transplanted plant out of the ground where the roots are then desiccated and the plant dies. For this reason, it is safer to transplant in the spring after the ground thaws in climates where frost heaving is a problem.

* Third, take precautions to preserve the integrity of the root ball. Tie the ball together and support it so it doesn't fall apart. The very safest approach is to dig a trench up to 12 inches deep, around the dripline of the plant. Then undercut the plant to form a cone, removing the soil an inch or so at a time, moving all around the plant, until you begin to see that you are removing roots. If possible, then get a square of burlap under the plant. Tilt the plant to one side, put one edge of the burlap close to the center of the plant, wadded up so that only half of it is on the open side of the plant, then rock the plant the other way and pull the burlap through. Tie the corners of the burlap to each other across the plant. Tie the burlap tightly to keep the soil around the plant roots undisturbed. Then lift the plant by the burlap and the bottom, not by its stems.
If the plant is very large it is important to dig a wide root ball. Don't worry about digging deep into the soil since most azalea & rhododendron roots are near the surface. Dig the plant, preserving a root ball as wide as can be safely moved. You can lift it onto a tarp and then use the tarp to drag the plant to its new location rather than picking it up. Be sure not to plant too deeply and water it thoroughly after transplanting.

* Finally, pruning the top helps match the demands of the top to the capability of the roots after they are stressed by the move. People have been known to cut the top off wild rhododendrons before moving and the plants have come back with superior shape. This is drastic and not recommended for a plant you don't want to risk loosing. Rhododendrons and azaleas have dormant buds beneath the bark which sprout to form new growth after severe pruning, hence severe pruning which removes 1/3 to 1/2 of leaf area is quite common when transplanting. Make sure you watch the plant after it was moved like you would a new plant. Its roots are compromised and it will need a reliable source of moisture. If the weather has a dry spell, make sure you water any newly planted rhododendrons, large or small.

If you prune now, you will still have flower buds next year.

Here is a link that might be useful: How to grow rhododendrons and azaleas.

I didn't root prune, just attacked with shovel. keep in mind that it will take a few hours of digging and it will be heavy. Had to cut a few roots that were thicker than my loppers, I used an electric reciprocating saw.
I was mildly surprised that it survived! I moved mine in late spring, a few weeks after flowering, did nothing special except top dressed w/compost and 4" hay mulch, I though it would need time to get ready for my cold winter. Maybe I was just lucky.

Root pruning is done by cutting down with a shovel in a circle around the plant several months before moving so the plant can establish a more dense root ball. It increases the chances of survival.

Thanks about to tackle same.