Need an IF/THEN cut and paste marco please...

thanks so much for your help so far. I am now using the following code:

Sub Copier()
rowz1 = Sheets(1).Range("B1").Offset(Rows.Count - 1, 0).End(xlUp).Row
rowz2 = Sheets(2).Range("B1").Offset(Rows.Count - 1, 0).End(xlUp).Row

With Sheets(1)
    .Select
    .AutoFilterMode = False
    .Range("A1").AutoFilter Field:=1, Criteria1:="<>"
    .Range("A2:R" & rowz1).SpecialCells(xlCellTypeVisible).Copy
End With

With Sheets(2)
    .Select
    .Cells(rowz2 + 1, 1).Select
    .Paste
End With

End Sub

So I am still facing the problem of duplicates. On the first tab, more information will be added on a weekly basis and then the second tab that this information is added to is a log of everything. So, I cannot use a macro that erases everything on the 2nd tab and pastes everything from the first tab.

My question is this, would it be possible to add to the above code to make it so that after the marco is run, an asterik is put in the H cell of the copied row AND when the marco is run, it will not copy and paste any row that has an asterik in the H column?

Is that too far-fetched? I have attached the file. Control + l TEST INVENTORYv2.xlsruns the above macro, however, as previously noted, if you press it again, it will copy all the same information plus any new information onto the 2nd tab. Any information that is on the 1st tab has to remain there so I cant delete it..

Thanks for your ideas/thoughts and codes!!