I have recently become aware that a co-worker is being harassed via anonymous Instagram messages. The harasser has cited in their direct messages that they do not like this person in the workplace, and has been sending messages to their ex-partner and a current partner of another staff member claiming that they have been having an affair and threatening to inform those around them at work that this is going on.
The victim, I and several others have a very strong suspicion as to who is sending these messages. They have noted on several occasions to multiple people that they do not like the person in question, and has also previously mentioned that this person is "sleeping around".
My thinking is that this is quite a serious offence and that something should be done, however the person in question has contacted HR which has prompted a company-wide email which makes no specific mention of the incident, rather directing people to the company Code of Conduct. Line managers have also been informed. I feel that this is not a strong enough action for somebody who is willing to do this, and could even bolster their confidence in not getting caught or investigated.
This person is willing to take other people's personal relationships into their own hands without any sort of evidence to back up their claims in order to justify some sort of work unpleasantness. That, I feel, should be punishable to some degree, or at least investigated further.
What is the correct course of action in this situation?