I would get some rubbing alcohol, (or maybe vinegar-isn't vinegar what kills mold on shower curtains?) and the sharpest shears I could find , or a box-cutter with spare blades, and cut 4 inches above and below the moldy section, and I'd throw that part away. Then I'd disinfect my shears, (or change my box-cutter blades with each cut I made) and cut both the rooted stem and the moldy top back to healthy wood, apply fungicide to both, and let them callus over, I'd try to root the top cutting later. The rooted stem should put out new growth if left alone.
This is what I'd do after checking with the experts on this site, first, since I'm a relative plumeria novice.
No need to give up on, or waste the moldy plant, but I would isolate it from any other plumeria you may have, as mold and fungus can spread.
I wish you luck, and am looking forward to pics of your other cutting's blooms
