They must also be made aware that it’s wrong to text, write or post anything that deliberately offends, hurts or otherwise harms anyone else in any way, including someone they don’t like – or don’t know. Make them aware of how they would feel if they were on the other end of such behaviour. Bullying can also result in defamation, punishable by law.
If on a computer, keep a record of the bullying message by using the ‘Print Screen’ key on your keyboard. If on a mobile device, take a screenshot to record and report the incident.
Also ... make sure your child knows they must guard their computer and mobile device with password or PINs so that even the most casual text message or email cannot be copied or hijacked and used to bully someone else in your child's name.
More information (from UK sources)