In an open letter
posted to Medium, Erica Lafferty called on Trump to "denounce (the theories) immediately and cut ties with Alex Jones and anyone who subscribes to these dangerous ideas."
"You've appeared on Jones' radio show, praised his 'amazing' reputation and promised him that you 'won't let him down,'" she wrote, making reference to Trump's appearance via video last December. "Now he's claiming you've personally called to thank him after the election, and will be on his show again soon."
Jones published a video last Friday saying Trump contacted him to offer his thanks and promised to come on the show again in "the next few weeks."
Trump spokeswoman Hope Hicks did not respond to an email asking to confirm Jones' account.
"On my way here, Donald Trump gave me a call," Jones said in the six-minute YouTube clip
"And I told him, 'Mr. President-elect, you're too busy, we don't need to talk.' But we still spent over five minutes (speaking), and he said, 'Listen, Alex. I just talked to the kings and queens of the world, world leaders, you name it.' But he said, 'It doesn't matter. I want to talk to you to thank you and your audience. And I'll be on in the next few weeks to thank them.'"
Lafferty, who supported Hillary Clinton during the presidential campaign, has become a vocal gun control activist. She denounced Sen. Bernie Sanders during the primary after he told the New York Daily News in an interview that he did not believe Sandy Hook families should be allowed to sue gun manufacturers.
Jones backed Trump during the campaign and relentlessly promoted the "Hillary for Prison" meme that became a common chant at the Republican candidate's rallies.
The Southern Poverty Law Center says Jones is "almost certainly the most prolific conspiracy theorist in contemporary America."
He is also one of the most successful, building a considerable fanbase with wild claims that the US government was behind the 9/11 attacks and that FBI agents carried out the 1995 Oklahoma City bombing.