Yes, the employer may appeal. First, try to appeal internally, through the board's own appeals or review process--depending where you currently are in the process, you may be entitled to ask them to review or reconsider their ruling. If that doesn't work, you can file a court case in county court appealing their ruling--you have the right to appeal agency decisions through the courts. Before doing so, note that this can be expensive--to have a reasonable chance of success, you should hire an attorney--and that the chance of winning is less than 50-50, since the courts tend to defer to the agency decision if it's arguably wrong, but could be right, they will uphold it only if there is clear error do they tend to overrule the agency. Therefore, depending on how much backpay is at stake, it may not be worthwhile going to this length.