  The Funk--Minkowski transform ${\mathcal F}$ associates a function $f$ on the
sphere ${\mathbb S}^2$ with its mean values (integrals) along all great circles
of the sphere. Thepresented analytical inversion formula reconstruct the
unknown function $f$ completely if two Funk--Minkowski transforms, ${\mathcal
F}f$ and ${\mathcal F} \nabla f$, are known. Another result of this article is
related to the problem of Helmholtz--Hodge decomposition for tangent vector
field on the sphere ${\mathbb S}^2$. We proposed solution for this problem
which is used the Funk-Minkowski transform ${\mathcal F}$ and Hilbert type
spherical convolution ${\mathcal S}$.
