Amazing heartless lie that's often been told (5)

I believe the answer is:

fable

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'amazing heartless lie' is the definition.
'fable' can be an answer for 'lie' (I've seen this in another clue). I am unsure of the 'amazing heartless' bit.

I don't understand how the rest of the clue works.

Can you help me to learn more?

(Other definitions for fable that I've seen before include "Old wives' tale" , "Mythological story" , "Myth, legend" , "It's not true" , "there may be a moral to it" .)

I've seen this clue in the Evening Standard.

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