Linear elasticity problem for a straight wedge disclination, which axially pierces a hollow sphere (a spherical layer), is solved analytically. The disclination displacements, stresses and dilatation are given in the form of series with Legendre polynomials. The related elasticity problems for a wedge disclination in a bulk elastic sphere and those one treading a spherical cavity are addressed, as well. It is demonstrated that the found solutions satisfy the boundary conditions on spherical free surfaces including the disclination emerging points. The distribution and the magnitude of the disclination elastic fields in spherical bodies strongly depend on the presence and the size of the inner cavity. For the correct treatment of elasticity for a disclination penetrating through a spherical pore, it is necessary to take into account strictly the boundary conditions on the remote external boundaries of the elastic body.