How can I make this macro print in other excel file?

Excel 2010
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I'm using this code to print user's accessing a file:

Private Sub Workbook_Open() 
With Sheets("Sheet2") 
lastrow = .Cells(Rows.Count, "A").End(xlUp).Row + 1 
.Cells(lastrow, 1) = Environ("Username") 
.Cells(lastrow, 1).Offset(, 1).Value = Now 
End With 
ActiveWorkbook.Save 
End Sub

However as someone could just delete the printed user log in the Sheet2, and also you can't use this if you protect the sheet, which defeats the purpose.

I want it to print the log into a separate file. Can I add in the file path/name to this code somewhere?

Thanks