Move very close to the funny coypus (4,2)

I believe the answer is:

cosy up

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'move very close to' is the definition.
I don't know anything about this answer so I cannot tell whether it can be defined by this definition.

'funny coypus' is the wordplay.
'funny' indicates an anagram.
'coypus' with letters rearranged gives 'COSY UP'.

'the' acts as a link.

Can you help me to learn more?

(Another definition for cosy up that I've seen is " Curry favour".)

I've seen this clue in the Sydney Morning Herald.

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