Accusations of lying hurt, especially when they are true, or worse when the lie is for the other person. Meaning if DH is caught sneaking to do something for me he is CRANKY. Humor and an appology for being nosy on my part usually gets him out of it.
Honesty is imoprtant, and so is trust. Why would a dude lie about having more money than usual? and why is he supposed to be so accountable to you? I mean yeah I want honesty, but I know when I was a kid the need to do homework never bothered me, the need for my parents to pester me about it did. I think at home I would be bothered the same way if DH felt the need to drag a confession out of me. BTW direct deposit if possible is a wonderful way to remove the whole question.
If you are really burning to know (or if you suspect something illegal) ask if you should either write a thankyou to the doner, or if maybe a some baked goods would suffice. He picks you deliver and find out the truth, if he doesn't pick then say you don't feel right accepting someting without thanks how about a joint prayer?
Generally for screaming I have found that screaming back is the most uneffective (err ineffective?) way to stop it, seconded by tears. Usually what works here is one of us gets calm, and hopefully rational, and asks exactly what are we mad about? Generally a guy will stop yelling if he is required to state outloud that he is mad cause tried to do something nice (or cause he is caught in a lie).
During any fight, try to stay on topic, finish dealing with the money, then worry about dirty socks strewn about.

(actually it sounds like socks are pretty low on the list, fortunatly you have a lifetime to work on it all)
If you are honestly thinking of foul play or something odd like that, look closly at the man you agreed to spend the rest of your life with, and be honest with him. Tell him your fears, and hope they are groundless, and IMO appologize for mistrust if they are If they arn't then you can focus on the real issue. Whatever it was he did that he felt the need to lie about.
When DH and I were newly married I had a silly theory about DH. I mentioned it to him and asked his help to get over it. He gladly supplied all the missing information and all the extra support I could want to get over it. I think if my silly fear was real, then he would have prolly noticed how it upset me, and how I assumed the BEST (trusting him), and would still have offered to help together get thru it. I didn't go accusing him, I went expecting the truth to be much better than my imagination, and it was as usual.
Oh on appologies, Men IME rarely ever give them voluntarily, but when asked for a specific appology IE "I am upest that you yelled at me, it would make me feel better if you appologized" Usually works. For me I am generally not done being mad till I get one,a nd I have a terrible habit of asking 'what for?' when I hear 'sorry' so I appologize first for my need and then get a full appology for whatever he is sorry for. Also the more you are willing to appologize for, the more a guy is often willing to appologize for. Humor helps here too. (I said sorry are you gonna? with a smile!)