Delivery note claiming son is "Gem of the Month" (10)

I believe the answer is:

birthstone

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'gem of the month' is the definition.
'birthstone' can be an answer for 'gem' (I've seen this before). I'm not sure about the 'of the month' bit.

'delivery note claiming son' is the wordplay.
'delivery' becomes 'birth' (the delivery of a baby).
'note' becomes 'tone' (synonyms).
'claiming' indicates putting letters inside.
'son' becomes 's' (genealogical abbreviation for son).
'birth'+'tone'='birthtone'
'birthtone' enclosing 's' is 'BIRTHSTONE'.

'is' acts as a link.

Can you help me to learn more?

(Other definitions for birthstone that I've seen before include "rock for one's arrival" , "emerald for May, perhaps" , "May emerald, say" , "Gem associated with zodiac sign" .)

I've seen this clue in The Telegraph.

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