On which to write a short letter home? (7)

I believe the answer is:

notepad

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'on which to' is the definition.
I can't tell whether this defines the answer.

'a short letter home?' is the wordplay.
'a short letter' becomes 'note' (synonyms).
'home?' becomes 'pad' (pad can mean someone's home).
'note'+'pad'='NOTEPAD'

'write' is the link.

Can you help me to learn more?

(Other definitions for notepad that I've seen before include "PC" , "Place for recording" , "Block of writing paper; computer" , "Where memos get written" , "writer's block" .)

I've seen this clue in the Evening Standard.

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