Rank is rank and a captain of any corp will always outrank a lieutenant of any other corp. A good captain will listen to the lieutenant (and NCOs) of the more relevant corp, and hopefully act accordingly.
The captain would remain a captain and likely remain in the USAF. They would however not be used in a combat role, at least not to begin with.
Chances are they'd be assigned to a supporting position, perhaps commanding a maintence unit and eventually be given some rudimentary infantry training.
As the war progressed, it's likely their entire squadron would be re-roled and undertake retraining in a similar way as some WWII infantry units were retrained as armour.
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If it moves, shoot it, if not push it, if it still doesn't move, use explosives.
Nothing happens in isolation - it's called "the butterfly effect"
Mors ante pudorem
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