A way of communicating I'm a liar, unfortunately (3,4)

I believe the answer is:

air mail

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'a way of communicating' is the definition.
I can't judge whether this definition defines the answer.

'i'm a liar unfortunately' is the wordplay.
'unfortunately' indicates an anagram (a bad or unfortunate spelling).
'im'+'a'+'liar'='imaliar'
'imaliar' anagrammed gives 'AIR-MAIL'.

Can you help me to learn more?

(Other definitions for air mail that I've seen before include "Post via plane" , "Overseas letter service" , "Overseas postage" , "Letters that are flown in" , "Overseas post option" .)

I've seen this clue in The Independent.

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