You have the right to appeal the denial, assuming you send in the request for the appeal within the time stated in the notice denying the benefits. At the hearing, the employer will have to prove that you were discharged for "misconduct." Misconduct generally means a substantial breach of a material duty owed to the employer that demonstrates a willful or wanton disregard for that duty and which tends to harm the business interests of the employer. At the hearing, you will have the opportunity to present evidence (documentary or testimonial) to establish that you were fired for reasons other than misconduct.
I find it is oftentimes useful to view the EDD's file a few days before the hearing to determine what the other side provided regarding the reasons for the termination. That may help you better prepare your arguments.
You can find useful Precedent Decisions at the EDD's website. Some of the cases may have similar facts to which you analogize your case.
Unfortunately, the fact that HR said they would not deny you UI benefits is of no help whatsoever. Employers do not decide whether the benefits are denied or not. Although the employer can help or hurt an employee's chances of obtaining benefits depending on what information they provide to the EDD, the decision to deny UI benefits rests with the EDD.
You may want to speak with counsel familiar with unemployment insurance claims to discuss the types of evidence you may want to present. Some law schools or pro bono clinics provide assistance to low income wage earners in unemployment insurance appeals.
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