Give a rise, but it's fraudulently concocted (5)

I believe the answer is:

putup

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'it's fraudulently concocted' is the definition.
I don't know anything about this answer so I cannot judge whether this works.

'give a rise' is the wordplay.
'give' becomes 'put' (I am not sure about this - if you are sure you should believe this answer much more).
'a rise' becomes 'up' (as a noun).
'put'+'up'='PUTUP'

'but' acts as a link.

Can you help me to learn more?

(Another definition for putup that I've seen is " Build - house".)

I've seen this clue in The Irish News.

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