A few comments regarding this in the thread. This surely impacts your ability to get action with AA.

Post above talks about making 5BB an hour just playing this hand but pretty rare to get a steaming player announcing they are AI and another player to wake up with a hand. Not hard to play very well in this situation.

Without the fantasy situation occurring you're watching cards hit the muck when you get excited here

Is there any sense in shoving PF vs. just raising? Looking like just a blunt move to isolate rather than necessarily a big hand? Depends on reads on how we think V would see it, I guess. But if we can rep "I like my hand HU vs. ATC, please go away" rather than "I have a big hand, please build a side pot with me," wouldn't we want to?

Or is V unlikely to bite given H's lack of previous aggression?

There is a whole lot of unjustified live poker speak ITT. 1: This is obviously a dream scenario where you want to get as much value as possible, therefore trying to extrapolate a long term win rate from a scenario you may see once is pretty damn funny.2:The term "not bad for one pair" is probably tatted on every OMC in history, and right up there with "I hate jacks" and "Ak is a drawing hand It's a standard idiom that ignores the scenario and ranges and puts you into a box 3: While you are ahead of the blind shove, said extrapolators are ignoring the fact that even a blind hand has 14.79 percent vs AA, so you can take that out of your "win rate".
In theory you should raise, but exploitively I would base my play on the spewiness of the lag. Is he Lag pre or post? does he get aggressive with air or draws? How bad does he want to get to even?
To sum it up,it depends...personally i would make it $150-$175, but from the sound of your current image any amount will get a snap fold.So playing AA I.P. vs a random hand and a moderate- weak ranged stuck L.A.G. with a SPR of around 4, sounds extremely profitable.But by all means, one pair is only one pair.