Air Accident Investigation
The Air Accidents Investigation Branch (AAIB) based at Farnborough in the UK investigates civil aircraft accidents and serious incidents within the UK, its Overseas Territories and Crown Dependencies. This means that if an aircraft accident, or serious incident, occurs in the Falkland Islands it will be the UK AAIB who investigate it. The link below will take you to the Air Accident Investigation Regulations:
https://www.legislation.gov.uk/uksi/2018/321/contents/made
The United Kingdom also maintains a formal agreement between the civilian and military accident investigation authorities.The latest version was signed in December 2022 and can be downloaded by clicking the attachment at the bottom of the page.
This agreement covers everything each agency commits to do for each other. One of the most relevant points is that it also details which agency would have primacy in the event of an accident involving both civil and military assets. It describes the various possible scenarios and provides clarity on how investigations would unfold.