From my experience, you can only make an IAP in an app with the ID that was used to buy that app. I tried to buy an IAP with my account, in an app bought with my dad's account, and it wouldn't work.
Restoring purchases, though, I don't know.
The reason I ask is because I had to make a new Apple Id and all my pinball arcade IAP were from the other Id. But if you buy something from the free version it transfers over to the paid version which is on my older Apple Id. Since it wouldn't let me buy the pro version of TOTAN on the paid app, I bought it on the free version and it transferred over to the paid version.
But if I ever have to restore the IAP it I'm not sure if it will work like that.