If the Radon transform of a compactly supported distribution f not equal 0 in R-n is supported on the set of tangent planes to the boundary partial derivative D of a bounded convex domain D, then partial derivative D must be an ellipsoid. The special case of this result when the domain D is symmetric was treated in [J. Boman, A hypersurface containing the support of a Radon transform must be an ellipsoid. I: The symmetric case, J. Geom. Anal. (2020), DOI 10.1007/s12220-020-00372-8]. Here we treat the general case.