I received this plumeria after my grandmother passed, it has been in a smaller pot but still thriving. It has been near the beach in California where the temps rarely go below 50.

I brought it further inland to my house in SoCal. right before winter I put it in a larger pot. Shortly after the temps dropped below 40F and its leaves turned brown and fell off. I put it in the garage for the remainder of winter. After a month in the garage, the tips of the plant became soft and black. I put it outside early March when the temps started to get warmer and watered it. About 20 days later the tips are still black and soft and there is no sign of improvement. Below the tips and the main stock are still firm, but the color is a dull green/brown.

Please any advice on how to save this plumeria would be much appreciated since it means a lot to me.

Relax It's just doing it's own thing & the plant looks otherwise Healthy ! The tips are _dead, but... you'll see some hidden side bumps start to swell & replace the black ends.

*STOP Watering until you see some active growth ! The Warm Sun will help it come back.

The good news is the plant itself will probably be ok. The bad news is you have lost this year's bloom potential.
I personally would remove the dead tips (break them off gently, they will usually break right below the dead bits) and then wait until they start making new tips.