Packet Liam and son flourished, they're incorrigible thieves (13)

I believe the answer is:

kleptomaniacs

I'm a little stuck... Click here to teach me more about this clue!

'incorrigible thieves' is the definition.
'kleptomaniacs' can be an answer for 'thieves' (kleptomaniac is a kind of thief). I am unsure of the 'incorrigible' bit.

'packet liam and son flourished' is the wordplay.
'and' means one lot of letters go next to another.
'flourished' indicates an anagram (I've seen this in other clues).
'packet'+'liam'='packetliam'
'packetliam' after 'son' is 'sonpacketliam'.
'sonpacketliam' is an anagram of 'KLEPTOMANIACS'.

'they're' is the link.

Can you help me to learn more?

(Other definitions for kleptomaniacs that I've seen before include "tea-leaves compulsively" , "Compulsive stealers" , "They keep stealing things" .)

I've seen this clue in The Telegraph.

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