"AIBU to want him to stop being so angry?"
Yes, frankly you are being VERY unreasonable. Your brother has every right to be angry. And of course he hates her - I'd bloody hate her too if she'd done that to me. And like him, I would probably have allowed her fraud to stand and not dobbed her in, because she would have gone to jail, been evicted and lost her job, and he is a good person who wouldn't wish that on his worst enemy, let alone a sister he once loved (but now, quite rightly hates).
And what does he get for this stunning level of compassion? His other sister (and presumably his mother too) "want him to let it go and forgive her". So one sister betrays him by committing fraud and stealing from him, and the rest of his family betray him by wanting him to "let it go". By downplaying the devastation he must feel. By dismissing the amount stolen from him because it was a present, he had neither earned nor saved it himself (what the hell difference does that make? He hadn't spent it yet, so he must have had plans for it and the money was HIS!).
And as for all this rigmarole about paying him back - of course he is rejecting repayment right now, because you lot are all making him feel that this entitles your sister to his forgiveness (she's not).
Might I suggest that your sister opens a bank account in his name - she's a bank clerk, she should know how to do this - and pays the money into that account. That way, when he is ready to forgive her - and she'll have to work damned hard to earn it, and accept his current hatred is justified - she can give it to him.
In the meantime, you and your mother have to get your act together and apologise to your brother. You have all behaved towards him in the most appalling manner, and given that you probably make it clear that you want him to "let it go" I'm not surprised " he goes into a foul-mouthed rant about how he hates her". Be grateful that he is not currently including you and your mother in his hatred yet.
"DP says that I underestimate the level of betrayal" - he's right. Listen to him. Then you might not drivel on about would it be too much for him to forgive and forget" , because YES, it bloody well is too much!
on your brother's behalf