But the pair fell out after Parker was kicked off the forum several years ago.
Since then Parker has sent dozens of emails, text messages and letters.
"I will not sit by as you attempt to crush what little I have left, I would rather slit your damn throat and be done with it.
"If you don't say a word, I'm warning you right now, you will die!" she wrote in a letter to Anelli in February 2010.
The FBI also alleged Parker left the author a voicemail message, telling her: "You just wandered into a f*cking trap."
This week, Parker refused to speak about the allegations.
"I can't actually talk about it, that's all. So you're just wasting your time," she told the Herald on Sunday. However, her parents Elizabeth and Shane Parker said their daughter had a mental health issue and they were working with health authorities on it.
According to the PopWrapped blog, Parker had an enormous picture of Anelli tattooed on her upper thigh and penned a sexually explicit, dominatrix-themed short story dedicated to the author.
Anelli's assistant said this week that the author was concerned for her and her family's safety and wished to "respect the integrity of the ongoing case" so would not comment further.
The FBI affidavit said the bureau launched a "stalking" investigation into Parker in 2009.
New Zealand police confirmed they had assisted US authorities at that time. Parker was arrested in New Zealand around December 2011.
She was charged with criminal harassment but earned diversion early last year. Yet the FBI said Parker continued contacting Anelli.
The agency said Parker sent a hand-written postcard to Anelli's' parents in Staten Island this January stating:
"Consider this your first warning before I come back and end you for good."
And in March, Parker allegedly told the author in another postcard: "I can't be denied forever, you will give yourself to me in bed one day. Else I will return to your home and flay you alive."
Parker will be arrested if she travels to the US.
