Amadeus–Stripe Flight Booking Integration

I have a flight-only booking flow powered by the Amadeus API and I want to bolt Stripe onto it so customers can move smoothly from selecting seats to paying—and so I can settle funds and issue invoices automatically. Concretely, the integration needs to:

• Pull live flight availability, fares and fare rules from Amadeus, then create the corresponding Order when the traveller confirms their itinerary.
• Run an immediate payment authorisation through Stripe at checkout, store the PaymentIntent ID against the Amadeus Order, and complete full capture once ticketing is confirmed.
• Listen to relevant Stripe webhooks so any failure, success or dispute immediately updates the Amadeus record and triggers the right follow-up.
• Generate a branded PDF invoice on successful capture and email it to the passenger along with the Amadeus e-ticket and itinerary.
• Send status-driven email notifications (authorised, captured, failed, refunded) to both the traveller and an internal operations mailbox.

I already have Stripe and Amadeus credentials ready; what I need from you is clean, well-documented code (preferably php) plus step-by-step deployment instructions so I can roll it into our existing stack. If you have prior experience with either Amadeus Self-Service APIs or Stripe webhooks, please highlight it—speed to production is important on this one.