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I don't know if this is possible with apps on iPad, but if the apps are still present on my old phone even when they are removed from app store, they get transferred if I select to not set up up my new phone as a new phone and instead use a safety copy on iTunes for my new device.

I have noticed that a few things have disappeared from my downloaded list in app store as well, but at least my receipt have still been present in my mail.
But for a few songs I bought a long time ago that's not the case, cannot find any proof of my actually buying them even if i used one of them as my wake up ringtone for several years. But that was just a few bucks, so it did not bother me as much.