vba iserting value with offset method & copying to new sheet

[Sintek]

Hi All

I have started a new post on this as the code has been improved drastically and I need assistance adjusting xlnitwit's below code.
What I need to achieve is:

1. To have the word "COD" inserted into column F of each row that matches TRow criteria before copying over.
2. Currently the rows gets copied over and over again to Range A2. I need it to copy to next rows down after the first copy.

Can anyone assist. Been at it all night and can't figure it out.

Sub Move()
Application.ScreenUpdating = False
Dim TRow As String
TRow = "20160908285"
With Sheets("Temp")
    With .Range("A1").CurrentRegion
        .AutoFilter 2, TRow
        .Offset(1).Copy Sheets("Hist").Range("A2")
        .Offset(1).EntireRow.Delete xlShiftUp
    End With
        .AutoFilterMode = False
End With
Application.ScreenUpdating = True
End Sub