You'll have to get the Customs stamps done at LHR because that's your point of departure from the European Union. Theoretically, this means that you can't check in at MAN anything that you're claiming the VAT for because the Customs officer would be within their rights to ask to see the item(s) at LHR. They don't usually ask to see the item, but it's hit or miss. The only ways around this would be 1) bring the VAT refund items in your hand luggage or 2) only check your bags through to LHR, claim them, show the items and get the Customs stamps at T5, then re-check your bags on to JFK.