Interesting how people are explaining different aspects, but not answering the question.
送る is not a change-of-state verb, so 送っている means "is sending", not "has sent". So you are right, the correct form for the situation you are describing is 送ってある (or simply 送った).
That being said, are you sure she did not say もう送ってる? I sometimes hear てる as a contracted form of てある (although probably not "correct" strictly speaking), but using ている for てある sounds quite unnatural to me.