"If you look at the Davis case, what Nasa is essentially saying is that lunar material in private hands is stolen property".
Still, the government could claim possession of the vial.
Ms Davis and her new husband met the "buyer" at a Denny's Restaurant, only to discover it was a sting operation lead by Nasa's Inspector General. "Lunar material is not contraband".
The vial has been tested by experts who have mixed reports on whether its contents consist of lunar dust, material from Earth, or a combination of both, according to the Post. Cicco said her father, Tom Murray, was friends with Armstrong.
"Neil Armstrong wouldn't have had the authority to give the moon rock away", he said. As some tests suggest a lunar origin and some did not, the expert noted that it might be a mixture of dust from Earth and the moon.
While the young girl kept the note with her, she couldn't keep a track of the vial and had not seen it in decades.
Armstrong's inscription on the back of the business card reads, "To Laura Ann Murray - Best of Luck - Neil Armstrong Apollo 11", according to exhibits submitted as part of the federal complaint.
The lawsuit, which Cicco filed this week in federal court, is a proactive measure to prevent NASA from attempting to claim the vial of dust. "She is the rightful and legal owner". NASA has not made any attempt to retrieve the vial from Cicco, nor has there been any confirmation by the space agency whether it plans to do it.
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The federal agents believed the 74-year-old had stolen the artefacts (she was never charged and successfully sued the agents).
Cicco's complaint cited a previous case involving an elderly California woman who accused Nasa officials of wrongfully seizing lunar mementos that her late husband, an Apollo programme engineer, had given her. Joann Davis said her husband left her two paperweights that contained a rice-grain-sized fragment of lunar material, or "moonrock", and a piece of the Apollo 11 heat shield.
In 2016, McHugh represented another local woman fighting for control over a NASA bag used to collect lunar samples.
Much of the moon is covered in a layer of bright dust called the regolith.
Of the 270 lunar samples given as gifts by the United States to foreign governments, about 150 are missing and many are presumed to have been sold on the black market.
Now, Cicco is challenging NASA to ensure the vial (whose size is equivalent to a lipstick) stays with her.
Cicco, who now lives in Tennessee, said she doesn't have the vial in her possession.