If your employer confirmed to EDD that you did not lie on your application then it would appear that your claim was denied for some other reason. In order to proceed, you need to file an appeal to have a hearing before an ALJ where it will be your burden of proof to show that you are eligible for benefits.
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When the Employment Development Department ("EDD") issued its decision, it likely did so on a document called a "Notice of Determination/Ruling." If you received this, you need to look at the upper right-hand corner to determine the date of mailing. This is important, because you have only 20 days from the date of mailing to file an appeal with the California Unemployment Insurance Appeals Board ("CUIAB").
If you are beyond the 20 days, you can still file an appeal, but you'll need to explain why it was late. You can still get a late appeal heard on the merits, but to do so, you'll need to show good cause for the untimeliness. "Good cause" can be established through a showing of some combination of (1) mistake; (2) surprise; (3) inadvertence; or (4) excusable neglect. The general rule of thumb is the longer the delay, the better the reason must be.
If the Notice of Determination/Ruling indicates that you were terminated for misconduct related to the work under California Unemployment Insurance Code section 1256, then the employer will have the burden of proving misconduct. In the event you appeal the decision and the employer does not go to the hearing, you will likely be successful. Even if the employer attends, you will have the chance to testify and present evidence in support of your position.
An experienced unemployment appeals attorney can help increase your chances of success upon appeal.