As long as the cambium layer isn't separated, you may have some success in splinting it.
I have saved several trees and shrubs broken by ice and falling limbs.
Get out the old standby "cure-all-ails"; Duct Tape!
Pull the two parts together and try to mate them as best as possible, taking care not to damage the cambium layer.
Secure the two parts together, by wrapping the tape as tightly as possible around the fracture. Overlap some undamaged wood on both sides of the break by several inches.
Support the broken part of the plant by trussing it to the undamaged portion, using some cordage, cotton, hemp or plastic, to remove the stress on the tape.
I prefer cotton, since it will deteriorate and later, fall off the plant. If successful. the two parts should begin to knit together during the growing season, not unlike a graft.
I leave the tape in place. In time, it too, will deteriorate and fall off.
You might consider taking a few cuttings from the broken part and rooting them.
Here's a link to Don Hyatt's method of rooting cuttings.
Rb

Here is a link that might be useful: Rooting Azalea & Lepidote Rhododendron Cuttings

If you don't want to root them yourself, Kathy VanVeen offers a very inexpensive rooting service. See the link below.

Also, when trying to mend the break, you are actually grafting the plant back onto itself. You don't need to cut the wood, since you are reattaching what broke, it will be an exact fit without cutting. What is even better than duct tape is grafting tape and grafting wax. The grafting tape allows for growth in the plant and doesn't strangle it. The grafting tape usually deteriorates after the graft succeeds and before the plant is strangled. The grafting wax is to seal out disease organisms.

Splice Graft
Grafting Tape
Grafting Wax

Here is a link that might be useful: Van Veen Custom Rhododendron Propagation