Your new MacBook Pro has your 2019 files that you want to copy to your old MacBook. Your old MacBook is NOT running Catalina, correct?
If this is true, you can copy the files from your new MacBook to your old MacBook. You do not need to export the files. You could not do this since, you can't access the program under Catalina.
Go to the following directory, copy all files/directories from new to old.
Mac: /Users/User/Library/Application Support/NCH Software/ExpressInvoice/Shared