Stamping the Duty simply means you paid the stamp duty/ import duty / lodgement fee etc.
I have to pay an import duty (Tax) when I import somethings and I can pay this via the Tax office or let the logistics company handle it for me (Which is better)

I pay my patent fees on-line when I lodge them. and then I get my form back with a beautiful gold stamp on it.

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Note added at 1 hr (2009-03-05 04:59:37 GMT)
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When you pay by the post there is a posted date stamp by the post office on the envelope, When there is a dispute of hours as to who lodged the patent first it is about time. Anything which is official and records a date is considered as verification of who lodged first.

This way someone who lives 1,000 klm away from the patent office has the same rights as someone who can walk in and lodge their patent as the posted date stamp on the envelope is verification it is lodged.

I lodged 9 patents last week and I keep a record of the time of payment and the time of lodgement. I missed out on one patent by 12 hours, So I know how serious recording lodging times are.

Also most post offices accept payment for Government services, I haven't tried patent payments there yet, as it is easier for me to pay online. this would also be "Post does stamping"
I would change the words so it is a bit clearer.

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Note added at 1 hr (2009-03-05 05:25:09 GMT) Post-grading
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Thank You