In accurate correspondence, what comes before my name and after yours? (10)

I believe the answer is:

faithfully

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'in' is the definition.
Both the definition and answer are adverbs. Maybe you can see an association between them that I don't see?

'accurate correspondence what comes before my name and after yours?' is the wordplay.
I cannot quite see how this works, but
'accurate' could be 'faithful' (similar in meaning) and 'faithful' is present in the answer.
'name' could be 'ly' and 'ly' is found in the answer.
No letters remain.
This explanation may well be incorrect...

Can you help me to learn more?

I've seen this clue in The Guardian.

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