From FAQ (Entire Question):
A newly built fighter can be placed directly on a newly built aircraft carrier. Can a newly built fighter be placed on an existing carrier, or can existing fighters be placed on a new carrier?
An existing fighter that is in the territory containing the industrial complex or that is in the sea zone where the aircraft carrier is built can immediately be moved onto a newly built carrier. New fighters, however, can’t be placed directly on existing carriers.
OOB Revised Rules: (Bolded by me)
Page 21 NCM… Air Units: Air units can land in any friendly territories. They cannot end their move in hostile territories or in any territories you captured this turn. Fighters can land on any friendly carrier, even those that move during this phase…
Page 22 Mobilize New Units… However, fighters can enter play on newly built aircraft carriers… Newly built carriers can enter play with fighters aboard, whether those fighters were built this turn or were already in the territory containing the industrial complex…
Therefore:
Newly Built Carrier:
- Existing fighter? Yes, if on land with industrial complex where carrier was built from. (OOB Rules) (Advantage from land. Allows movement from land to sea thus gaining one movement point.)
- Existing fighter? Yes, if on existing carrier in Sea Zone where newly built carrier was built. (FAQ) (Advantage from sea. Allows transfer of fighter from non-phasing existing carrier to phasing newly built carrier. Example. US fighter on UK carrier moves from existing UK carrier to newly built US carrier freeing up slot on UK Carrier.)
- Newly built fighter? Yes. (OOB)
Newly Built Fighter:
- Existing carrier? No. (OOB)
- Newly built carrier? Yes (OOB)
(Andrew’s Note: The FAQ introduced a new rule that was not present in the OOB rules; that an existing fighter on an existing carrier in the same sea zone where the newly built carrier was placed in could move the existing fighter between the existing carrier to the newly built carrier.)
(It should be noted also this is for OOB rules only. In LHTR 1.2 the rules were amended to 1) allow a freestanding fighter to hover in a sea zone waiting for a newly built carrier and 2) removed the ability to move a fighter from a territory to a newly built carrier.)
(LHTR 1.2) Exception to normal fighter landing spaces rules: Your fighter may also end its move in a sea zone adjacent to an industrial complex you own if you have purchased an aircraft carrier that turn and will subsequently place that carrier in the seazone where your fighter ends
its turn.
Newly built fighters can be placed into territories containing an industrial complex controlled by your power from the start of your turn, or they may be placed on an aircraft carrier owned by your power in a seazone adjacent to a territory with such an industrial complex. The aircraft carrier may be an existing one or it may be a newly built carrier. You may not place a new fighter on a carrier owned by a friendly power. (Andrew’s Note - no mention of a fighter already in the industrial complex territory)
(Andrew’s Note: Finally, the LHTR 1.2 rules were unchanged regarding this specific discussion in LHTR 2.0.)