Copy Cell to another column on change - excel

Question

I need to copy the contents of a cell in a particular column to another corresponding column on change so the old value is moved. Only wants to work for a particular column.
Private sub Worksheet_Change(ByVal Target As Range)
if Target.Range("L:L") then
'set I cell value = to original L cell value
ActiveCell.Offset(0,-3).Value = ActiveCell.Value
End If
End Sub

Answer 1

This code should do what you want. Please take note of the comments which explain some limitations I have imposed on the action of this procedure. The rule to follow is to not give it more power than it needs to do the job you want it to do.
Private Sub Worksheet_Change(ByVal Target As Range)
' 027
Dim Rng As Range
' don't react if the changed cell is in row 1 or
' if it is more than 1 row below the end of column L
Set Rng = Range(Cells(2, "L"), Cells(Rows.Count, "L").End(xlUp).Offset(1))
If Not Application.Intersect(Target, Rng) Is Nothing Then
With Target
' skip if more than 1 cell was changed
' meaning, exclude paste actions
If .Cells.CountLarge = 1 Then
.Offset(0, -3).Value = .Value
End If
End With
End If
End Sub

Answer 2

This will save the previous value in column I:
Private Sub Worksheet_Change(ByVal Target As Range)
Dim v As Variant
If Target.Count > 1 Then Exit Sub
If Intersect(Range("L:L"), Target) Is Nothing Then Exit Sub
With Application
v = Target.Value
.EnableEvents = False
.Undo
Target.Offset(0, -3).Value = Target.Value
Target.Value = v
.EnableEvents = True
End With
End Sub
EDIT#1:
To update L without triggering the event, use something like:
Sub ScriptThatUpdatesColumn_L()
Application.EnableEvents = False
Range("L5").Value = "just me"
Application.EnableEvents = True
End Sub