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Pick the yes/no field in Odoo that marks an invoice as printed (the one in your Excel's "Print" column).
An invoice is NY when its Odoo company, or the customer's company, contains one of these words (separate with commas). Everything else is NJ.
Invoices from this date on that are not checked (green or red) keep showing in "To check", whatever day you look at. Red ones stay in Pending until solved, whatever their date.
Everyone needs an Odoo account. One login (e-mail) per line. Changes apply immediately.
Everyone not in these two lists sees both NJ and NY.