I am asking if it is possible to transplant a well established rhododendron.
Yes, you can transplant a large rhododendron with some care and work.
In cold climates you should move the plant in early spring.
Care needs to be taken to dig up as much of the root system as possible.
The shrub should be pruned back by about 1/3 to help the plant with stress.
Take your time in digging up the shrub and use a good sharp shovel to dig us the root ball. Move the root ball unto a tarp to move the shrub to the new planting hole.
Have the new hole prepared to make the transition quickly and efficiently.
Water the shrub well for first few weeks.