Thanks again all. @ Thai Kiwi - Just checked the ticket stock and for all legs - Edin to London, London to LAX, LAX to Auckland and Auckland to CChurch all the Eticket information starts with 086- XXXX. Same number on all 4 legs. So, not that she'll be wanting to do this for the foreseeable, any ideas or suggestions as to what's happened.
How can BA in Edinburgh and United in London check-in desks confirm she is booked on the NZ LAX to Auckland connecting flight, her baggage is also booked on it and travelled, yet Air NZ desk in LAX claim to not have her in the system ?