I read your other thread. I'm sorry to hear what you are going through.
As far as the receipt, I would address it with him when you are calm. I don't believe in combating dishonesty with further dishonesty. If he is being dishonest about having an affair, your being dishonest about finding the receipt is not the way I would go. I'd ask him about it, with an open mind. His response will tell you all you need to know. It may not be at all what you think, but at least it will be out in the open.
I seriously doubt that, if there is another woman, she can hold a candle to you. A woman that would have an affair with a married man is a broken person at best. She's a diversion (if she exists), something to pump up his ego. It's really not about her, but how she makes him feel about himself. It's all a fantasy, but it's a dream they don't want to wake up from. In the fantasy they're seen as perfect, unlike the real world where they have flaws.
Keeping your emotions in check will be key in getting him back. You don't want him to get the impression that your M is beyond repair. You want to have boundaries, but do not issue ultimatums. He must feel safe with you, and he must also respect you.
If there is an A, and it comes out into the open, it removes a lot of the allure from it.