al final me salió he hice esto..
Código:
Private Sub Button1_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Button1.Click
Me.lstCopiado.Items.Clear()
For Each item As Object In Me.LstCapitales.Items
Me.lstCopiado.Items.Add(item)
Next
Me.LstCapitales.Items.Clear()
End Sub