Great elm rotting: that's the message (8)

I believe the answer is:

'the message' is the definition.
(telegram is a kind of message)

'great elm rotting' is the wordplay.
'rotting' indicates anagramming the letters.
'great'+'elm'='greatelm'
'greatelm' anagrammed gives 'TELEGRAM'.

'that's' acts as a link.

(Other definitions for telegram that I've seen before include "Message sent by wire" , "It may bring word" , "(Old) type of message" , "Pre-1980s electronic message" , "Electric message" .)

I've seen this clue in The Sun.

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