Tamara,
Fluorite vs. Amethyst? Also, Hackmanite will change color under UV and retain the darker purple for a few minutes up to a few hours, before turning back to a light pink/lavender.
If I remember Amethyst does fluoresce under UV. What instruments do you have available?
https://www.mindat.org/min-1789.html Hackmanite. You can also view information on the Amethyst and Fluorite at this site if the other links are not available.
I would do a Specific Gravity test on each one separately.
Fluorite Specific Gravity: 3.180; massive material with impurities 3.0-3.25.
Amethyst Specific Gravity: 2.651
This would help identify one group from another. I would also keep tabs on which one’s colors changed over time. That is a unique trait.
-Troy