There is not a lot of detail here, but as the law stands and I understand it a conditional discharge has to be accepted by both parties. This assumes your friend accepted the courts decision; otherwise it would have gone to trial. Appealing a sentence is complicated and can be expensive. If your friend has, as I propose, accepted the conditional discharge I would assume it would be difficult to appeal. If it is threatening her livelihood or current position, then she should take legal advise from a professional, i.e. a solicitor. It might be grounds for appeal.