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It looks like an Alexandrite to me. Alexandrite does fluoresce under UV light, and its color varies depending on whether it’s in daylight or artificial light. It’s a beautiful stone. Mohs hardness of 8.5, so it’s pretty durable, but if it’s a large stone and was worn a lot over the years, I could see it getting a few dings on the girdle.
The first idea of the jeweler was amethyst, but then she commented it is quite pink for an amethyst (atypical, but not impossible). She was quite surprised seeing the intensity of the glow though. My current uneducated guess is a bi-colour colour change sapphire.
My next guess would have been Kunzite, but it looks like Kunzite glows more orange under UV light. Also, Kunzites that deep in color are pretty rare.