This issue is discussed in an interview posted some days ago: Watch “Murali Doraiswamy - How Does Memory Work?” on YouTube.
From what I understood from this interview, the current consensus about were information is stored is basically: everywhere in the brain, but nobody knows how it is done precisely. Short term memory appears to be mostly stored in the hippocampus and according to the person being interviewed, some of that information is transfered in tiny little pieces all over the brain. He didn"t seem very confident about when this transfer takes place; repetition and importance for survival seem to be possible triggers of this transfer, but no one really knows, it seems.