Copy columns based on header (Without header)

Does this help?

Sub Michael_BU()
Dim i As Long
For i = 2 To Range("A" & Rows.count).End(3).Row
Range(Cells(i, 1), Cells(i, 13)).Copy Sheets("INPUT").Range("A" & Rows.count).End(3)(2)
Next i
End Sub

Well, this will copy all the columns, but if the column order in the 2 sheets is different, then it will not work correctly I suppose.
Any solutions for that problem?

Try:

Sub Michael_BU()
Dim i As Long
Dim z As Long
Dim x As String
Dim y As Range
With Application
    .ScreenUpdating = False
    .Calculation = xlCalculationManual
End With
For i = 2 To Range("A" & Rows.count).End(3).Row
    For z = 1 To ActiveSheet.UsedRange.Columns.count
    x = Cells(1, z).Value
    Set y = Sheets("INPUT").Rows(5).Find(x, LookIn:=xlValues, lookat:=xlWhole)
    If Not y Is Nothing Then
    Cells(i, z).Copy Sheets("INPUT").Cells(Rows.count, y.Column).End(3)(2)
    End If
    Set y = Nothing
    Next z
Next i
With Application
    .ScreenUpdating = True
    .Calculation = xlCalculationAutomatic
End With
End Sub