The answer is actually fairly simple, and is the same in the box rules and LHTR, with one small exception.
When a territory changes hands, the ownership of any IC and/or AA guns in that territory changes with it. Whoever gains control of the territory gains control of the IC and/or AA guns IC. It doesn’t matter who the original owner of the AA gun or IC was.
The small difference between OOB and LHTR concerns situations where territories have been captured when they would have otherwise been liberated because a capital was under enemy control. Say Russia and Karelia have been captured by Germany. If the US captures Karelia, it gains control of the territory because the Soviet capital is enemy-held. It also gains control of any IC and/or AA guns there, because control of these transfers with control of the territory. If the US then liberates Russia, control of Karelia (along with any other territories held by allies) reverts to the USSR. Control of any ICs in these territories also reverts to the USSR. Under the OOB rules, the USSR would also gain control of any AA guns in these territories. Under LHTR, the AA guns would remain under the control of the country that captured the territory (the US in Karelia’s case).
In an attempt to forestall the inevitable arguments that come up with this topic, I’ll post a link to a previous discussion:
http://www.axisandallies.org/forums/index.php?topic=10974.0