I don’t believe so. I can’t imagine that anyone would check the serial numbers and notice they were the same if you were just, say, paying with three or four $20 bills in a store. If the bills passed the forgery test, nobody would notice the numbers, especially if they were not obviously bank-fresh.
However, if you turned up at a bank wanting to pay in a few thousand in bills with identical numbers, I think you’d be found out.
Ok, here’s a twist - the box has an inlaid design on the lid that looks like an ornate arrow. This design can actually be rotated so that the arrow either points to the edge of the box that has the hinges, or towards the opposite edge that doesn’t have the hinges. For brevity’s sake, let’s arbitrarily call these two directions “north” and “south” respectively.
When the arrow points “north”, the box duplicates items in exactly the way I’ve described in the OP. When the arrow points “south” however, the box instead *obliterates *anything placed inside. this process leaves absolutely no trace, the item vanishes completely and utterly, and it is not retrievable by any means. Once it’s gone, it’s gone. The box will only operate in either of these two modes if the arrow is pointing fully north or fully south - if it’s off by even a millimetre either way, the box does nothing.
So *now *what are the possibilities?