Germany attacks England with transports(loaded with infantry) and overland fighters, captures the territory. Can the fighters stay in England or need to fly back to mainland?
Attacking aircraft can never land in a newly captured territory. Being an amphibious assault does not change this rule.
The fighters need to return to a territory that was friendly since the beginning of the turn. Note that if the aircraft return to a land territory, it does not need to be the same one that they departed from. Fighters can also choose to land on an aircraft carrier. A single carrier can support two fighter planes.