If you don't have data in row 2, you will keep pasting to the same column until you do, then you will move across one.
Does this version work:
Sub ProcessWorkbook(wbk As Workbook, wbkDest As Workbook)
Dim Letter As String
Dim rngDest As Range
Dim wksDest As Worksheet
Dim iCol As Long
Letter = wbk.Sheets("Results").Range("A2").Value
Select Case Letter
Case "A", "C", "M"
Set wksDest = wbkDest.Sheets(Letter)
Case Else
Set wksDest = wbkDest.Sheets("Else")
End Select
With wksDest
If Len(.Cells(2, 1).Value) = 0 Then
iCol = 1
Else
iCol = .Cells(2, .Columns.Count).End(xlToLeft).Column + 1
End If
Set rngDest = .Cells(2, iCol)
End With
wbk.Sheets(2).Range("A1:A30").Copy
rngDest.PasteSpecial Paste:=xlPasteValues, Operation:=xlNone, SkipBlanks:=False, Transpose:=False
End Sub
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