I've noticed that this board is really quiet during the Northern Hemisphere Winter. I am not a plumeria expert, but I would consider myself knowledgeable in general.

Here's what I would do; because I would want both the seed pod, and the cutting to survive.

I would start rooting this cutting. As long as you keep it somewhat warm inside, it should be fine. You can root it in a small see-through container, or use the ziplock bag method. Just try to keep it warm, and do not move it at all until you see roots and it should root.