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It is clear that Group 1 metal fluoride salts DO NOT readily form solutions in organic medium. The amount of solvation that can occur leading to the eventual release of a fluoride ion depends on many factors, one is the polarity of solvent (described by dielectric constant). Most examples seen in the literature seem to evolve around using $\ce{CsF}$ or $\ce{KF}$ in the vicinity of 18-crown-6 ether as common examples for the release of fluoride ions (not considering TBAF). However, I cant seem to find any description for $\ce{MgF2}$ or $\ce{CaF2}$ salts and how their solubility in organic medium affects the release of fluoride ions.

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Don't get your hopes up. Wikipedia identifies magnesium fluoride as insoluble in ethanol. Calcium fluoride fares no differently in acetone. While these data are hardly exhaustive, they suggest strongly that Group 2 fluorides are not a good way to get fluoride ions into solution. Of course, we would not expect Group 2 ionic compounds with their doubly charged ions to get very far in organic solvents generally.

Getting fluoride ions into solution with organic solvents is typically done with bulky 1+ cations, such as N,N,N-trimethyl-(2,2-dimethyl-prop-1-yl)ammonium ion, $\ce{C_{8}H_{20}N^+}$. See Reference [1] as an example. The use of cryptand-complex alkali-metal complexes fits this paradigm because such ions are also bulky.

Reference

1. Victoria K. Davis, Stephen Munoz, Jeongmin Kim, Christopher M. Bates, Nebojslš a Momčilović, Keith J. Billings, Thomas F. Miller III, Robert H. Grubbs and Simon C. Jones, "Fluoride-ion solvation in non-aqueous electrolyte solutions", Mater. Chem. Front., 2019, 3, 2721

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