The following VBA code bellow, works perfectly.
However, I would like to ADD other functionality to it.
If the original loop completes and in all cells it finds that
If wsQuotes.Cells(cell.row, 5).Value = wsRequest.Cells(Target.row, "E").Value IS FALSE
And wsQuotes.Cells(cell.row, 6).Value = wsRequest.Cells(Target.row, "F").Value IS ALSO FALSE
Then find the next blank cell in column A of sheet 'QUOTES' and using that row, do the following
ThisWorkbook.Sheets("QUOTES").Unprotect Password:="edit"
                        wsQuotes.Cells(cell.row, 1).Value = wsRequest.Cells(Target.row, "A").Value ' CONTRACTOR
                        wsQuotes.Cells(cell.row, 2).Value = wsRequest.Cells(Target.row, "B").Value ' JOB
                        wsQuotes.Cells(cell.row, 3).Value = wsRequest.Cells(Target.row, "C").Value ' SECTOR
                        wsQuotes.Cells(cell.row, 4).Value = wsRequest.Cells(Target.row, "D").Value ' SUBSECTOR
                        wsQuotes.Cells(cell.row, 5).Value = wsRequest.Cells(Target.row, "E").Value ' QUO/INV#
                        wsQuotes.Cells(cell.row, 6).Value = wsRequest.Cells(Target.row, "F").Value ' VALUE
                        wsQuotes.Cells(cell.row, 7).Value = wsRequest.Cells(Target.row, "G").Value ' LOCATION
                        wsQuotes.Cells(cell.row, 8).Value = wsRequest.Cells(Target.row, "H").Value ' NOTES
                        wsQuotes.Cells(cell.row, 9).Value = wsRequest.Cells(Target.row, "I").Value ' P REQUEST#
                        wsQuotes.Cells(cell.row, 10).Value = wsRequest.Cells(Target.row, "J").Value ' DATE
                        wsQuotes.Cells(cell.row, 13).Value = "Finance"
                    ThisWorkbook.Sheets("QUOTES").Protect Password:="edit"

Here is the original VBA event:

Sub SearchSubmittedQuotes(Target As Range)

    Dim wsRequest As Worksheet
    Dim wsQuotes As Worksheet
    Dim cell As Range
    Dim searchValue As Variant
    
    ''''If ActiveCell.Column <> 7 Or ActiveSheet.Name <> "PREQUEST" Then
    ''''Application.EnableEvents = True
        ''''Exit Sub
    ''''End If
    
Application.EnableEvents = False
    Set wsRequest = ThisWorkbook.Sheets("PREQUEST")
    Set wsQuotes = ThisWorkbook.Sheets("QUOTES")
    
    wsQuotes.Unprotect Password:="edit"
        searchValue = Target.Offset(0, -7).Value
        For Each cell In wsQuotes.Range("A5:A" & wsQuotes.Cells(wsQuotes.Rows.count, "A").End(xlUp).row)
            If wsQuotes.Cells(cell.row, 1).Value = searchValue Then
                If wsQuotes.Cells(cell.row, 5).Value = wsRequest.Cells(Target.row, "E").Value _
                    And wsQuotes.Cells(cell.row, 6).Value = wsRequest.Cells(Target.row, "F").Value Then
                    ThisWorkbook.Sheets("QUOTES").Unprotect Password:="edit"
                        wsQuotes.Cells(cell.row, 8).Value = wsRequest.Cells(Target.row, "H").Value ' NOTES
                        wsQuotes.Cells(cell.row, 9).Value = wsRequest.Cells(Target.row, "I").Value ' P REQUEST#
                        wsQuotes.Cells(cell.row, 10).Value = wsRequest.Cells(Target.row, "J").Value ' DATE
                        wsQuotes.Cells(cell.row, 13).Value = "Finance"
                    ThisWorkbook.Sheets("QUOTES").Protect Password:="edit"
                End If
            End If
        Next cell
                Target.AddComment "Quote sent to Finance " & Date
            wsQuotes.Protect Password:="edit"
    Application.Wait Now + TimeValue("00:00:01")
    'Application.EnableEvents = True
    ProcessQuote Target

End Sub