Crossword Genius

By inference, more off message? (6)

Ross

I believe the answer is:

lesson

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'message?' is the definition.
(lesson is a kind of message)

'by inference more off' is the wordplay.
'by' is a charade indicator (letters next to each other).
'inference more' becomes 'on' (I can't justify this - if you can you should give a lot more credence to this answer).
'off' becomes 'less' (I've seen this in another clue).
'on' after 'less' is 'LESSON'.

Can you help me to learn more?

(Other definitions for lesson that I've seen before include "Sermon or teaching session" , "Seminar" , "Piece of instruction" , "Reading or exercise for a pupil" , "Single period of instruction" .)

I've seen this clue in The Guardian.
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