I haven’t found anything earlier that brings up this question, but although the resolution was clever, it didn’t satisfy me, and (though I could be wrong) I think Brown misses the fact that at one point there should be two copies of the object in existence at the same time. In any case, this was the first part of a pair of short-short stories in the Feb ’54 Galaxy, which together were called Two-Timer (the second of which had no time travel).