You are joking, right? Even if she believed it was a joke, reading this thread would probably change her mind and be pissed at him (or at least at herself for believing him)
Speaking only for myself, I thought it was pretty clear from the first post that the “spiders in the lab” thread was not on the level and I found those who took it seriously to be over-reacting and frankly kind of . . . well, let’s go with “short-sighted.” But you still make a great point: Once you’ve made a stupid suggestion or done a stupid thing, you can’t really successfully fall back to “IT WAS A JOKE!” because even if it really was a joke, some people won’t believe you and will think you’re just making a lame excuses, because “it was a joke” is the classic lame excuse.
IOW, there’s no way to distingish “it was a joke” (the lame excuse) from “it was a joke” (the honest-to-God reality), and so there’s no way to know if Otto’s friend will believe him when he tries to explain to her that he was kidding around. I’m inclined to think she won’t believe him, because there is nothing funny about taking someone’s money without their permission. I wouldn’t believe you, Otto, sorry.
So much as it pains me to say so, given that I’m usually in the “honesty uber alles” camp, I would not 'fess up, because 'fessing up looks and sounds too much like “I was stealing from you and you caught me.” I would hope the matter would just blow over, relying on the fact that she’s not 100% certain it was you (you hope) and is willing to give you the benefit of the doubt. I would try very hard to be an honest, good, and unstupid friend to her in future, so that she must think to herself “surely my honest, good, unstupid friend Otto could not have taken it, he would never do something like that!” And I would make damn sure I never did anything like that again.
So how do you return the money then? the “try[ing] very hard to be an honest, good, and unstupid friend to her in future” can still be implemented after admitting the truth. By not admitting, he runs the risk that she knows he stole the money because someone that she does trust told her “I saw Otto taking something out of the jar” after she started investigating.
I dont think there is a good answer here, but I would say that, as long as there remains a little doubt about whether he took the money or not, it would be possible to repair the friendship over time. If he admits it, there will no longer be that sliver of plausible deniability, and I don’t think he would ever emerge from the “thief” classification he’d have from then on. Not the ideal way to save a friendship, but the only one I can see. And of course he has to get the money back to her, anonymously, which could be tricky.