
Contact the Cargo side of the airlines that go from your nearest airport to their nearest get a quote an Bob's your uncle.
We sent a pup with Delta from Heathrow to New York (JFK) and it was just over £500.
You will also need to buy an airline crate (we bought a larger size so it would continue to be useful to pup until adult), and also you will need to get health certificate.
If pup is under 12 weeks ti won't require Rabies or any vaccinations, though ours went out at 11 weeks with full puppy vaccs minus Rabies.
I t might work out cheaper for new owners to collect pup and take it back with them either in cabin(if small enough) or in hold as excess baggage which is a fraction of the cost of Cargo.