I agree that it should be reported to the police. You want to fully document the incident. In addition, it would be helpful to print out the posts and stick them in a file. If harassment continues, you want to be able to establish a clear pattern of behavior over time. This would facilitate getting a restraining order in the future, for example, if that were to become necessary.
It makes more sense to learn to cope with internet
trolls. It's a lot of effort to document incidents, call
the cops, & build a case, when it'll come to naught.
It's the wrong focus.
The best approach is to manage one's own feelings,
thinking, & conduct. Of course, if ever a threat looks
potentially something that could be acted upon,
then it's worth contacting authorities.
BTW, in social media (even RF) I've been threatened,
& told to die in most grisly fashion. My reaction was
meh....ie, see them for what they are....a foul person
raging from the safety of internet anonymity.
But I still observe some caution. I use my real identity
only on a few sites where everyone else does too, &
we're all civil with each other.