I expect as an attempt at stock control the steerer starts of with x thousand ltrs of fuel, a starting counter number on the pump, x bags of coal and x numbers of whatever other stuff they sell. Each transaction is entered in a book with meter readings opening and closing from the pump.
Upon return to base a closing stock take is done which when subtracted from the opening gives the value of stock presumably sold.
That value should equal the amount of cash carried and cheques, plus electronic payments received.
If the shortfall was £X xp. Then a gander through the sales book for that amount arrived at Arthur. I expect it was his transaction that's at the bottom of it, but not Arthur himself. Upon questioning the steerer has only two options, pay out of his own pocket or recall that Arthur didn't pay.
I shouldn't pay twice.