That's not terribly relevant for Internet applications, because for the most part people deliberately cause the computer they control to download and save copyrighted material to storage they control, and then consume it at leisure. That's copying.

That still means you'd have to show the user actually made a copy themselves - that's different than learning they possess one.

If I understand right (I'm not a lawyer), something like this came up in a case about a utility for cheating in an online game, and another much older one about the copy of an app made in memory in order to run it.

For the purpose for which the software was sold and bought, the in-memory copy is legit[1]. For cheating, it's a copyright violation[0].

[0] https://www.engadget.com/2008-07-15-blizzard-wins-lawsuit-ag...

[1] http://digital-law-online.info/lpdi1.0/treatise20.html