Yet another VAT refund question

I have read multiple topics related to VAT refund and still have a few questions regarding the refund process.
I plan to purchase a new purse in Paris but will be returning to US from Rome with transit in Heathrow airport. I think I'll only have 2.5 hr transit in Heathrow. Does this mean I have to request the VAT refund in Heathrow because it's the last stop (though it's only transit)? Would I have enough time? Are there VAT refund agencies in Heathrow after immigration & custom?

I'd really appreciate any help in this matter. Thank you. :)

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