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I don't think there's a rules answer.
I'd let you try, but you'd need to make some kind of check - probably Sleight of Hand - to place the item in such a way that the shifting of the elemental material as the familiar moves doesn't reveal the item. Might also apply some penalty to the familiar since having a large foreign object inside you has to be distracting at best. Shaken or sickened sounds about right.
I think abilities which conjure things like that displace matter that is in the way.
I don't know about "while it's forming" but if a geokineticist forms a hedgehog familiar, it's not an actual hedgehog and doesn't need to eat or breathe like a normal one does, so I don't see why you couldn't get it to just swallow an item of appropriate size for safe-keeping.
For some elements you're going to have a problem though (the fire hedgehog swallowing the piece of paper isn't going to go well, and water, aether, and air are going to be kinda transparent.)