If your boss cheats and lies to customers, you don't want to work long term for him. Not only is this routine a direct indicator that your business is in serious financial trouble, but your boss probably cheats you too in small ways. In the meantime, stop participating in routine lies. If he gives you a fraudulent invoice to process, let him know you're concerned about answering customer questions when they notice something amiss. In talking with your boss, keep your cool.
Honesty mixes better with diplomacy than with tactlessness.
Since the truth in this situation is negative, frame it as an issue of concern rather than an attack. Tell your boss that you are experiencing confusion over some of the invoicing and you would like his direction. Ask him questions about the charges and ask his reasoning on the finance charges. Point up the fact to him that you have spoken with customers who have mentioned they were invoiced incorrectly. In short, give your boss has a way out and make the quickest exit you can out of this company.