Frangipani Stem Rot

I have recently moved house and have inherited a mature (2.5m) Frangipani tree with possible "stem rot".
The plant was moved 1.5 years ago by the previous owners.
The top 15cm of growth is fine then growth is "spongy" for approx 10cm and then below this the growth is fine again.
Now I have recently transplanted the same tree again!
I do not know if I should prune off the "spongy" bits (is this stem rot from the previous move?). The plant is now dormant with a few very small leaves left at the tips.
Should I prune it back to below the "spongy" areas? If so, can I prune it now in winter?
Thanks, any information is appreciated!

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