If Not Intersect(Target, Range("A1")) Is Nothing Then
this line is what triggers the code, it's looking for a cell value change in the specified range (A1). To extend the range change A1 to..... A1:A10000.....or A1:Z1.....or A1:Z10000, whatever range is needed.
However, the code to copy bits around is done with:
lCol = Cells(1, Columns.Count).End(xlToLeft).Column
Cells(1, lCol + 1).Value = Range("A1").Value
this only looks for the next available cell in row 1. In order to make this copy to the next available cell of whichever row was just changed, change it to:
lCol = Cells(target.row, Columns.Count).End(xlToLeft).Column
Cells(target.row, lCol + 1).Value = Range("A" & target.row).Value
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