Thus prime minister accepts his fallacious argument (7)

I believe the answer is:

sophism

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'fallacious argument' is the definition.
'sophism' can be an answer for 'argument' (I have seen 'False argument' mean 'sophism' so perhaps 'argument' could also mean 'sophism'). I am not sure about the 'fallacious' bit.

'thus prime minister accepts his' is the wordplay.
'thus' becomes 'so' (synonyms).
'prime minister' becomes 'PM' (abbreviation).
'accepts' is an insertion indicator.
'pm' enclosing 'his' is 'phism'.
'so'+'phism'='SOPHISM'

Can you help me to learn more?

(Other definitions for sophism that I've seen before include "False argument" , "faulty reasoning" , "specious argument" .)

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