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In this paper, we derive analytical expressions for the leading-orderhydrodynamic mobility of a small solid particle undergoing motion tangential toa nearby large spherical capsule whose membrane possesses resistance towardsshearing and bending. Together with the results obtained in the first part(Daddi-Moussa-Ider and Gekle, Phys. Rev. E {\bfseries 95}, 013108 (2017)) wherethe axisymmetric motion perpendicular to the capsule membrane is considered,the solution of the general mobility problem is thus determined. We find thatshearing resistance induces a low-frequency peak in the particle self-mobility,resulting from the membrane normal displacement in the same way, although lesspronounced, to what has been observed for the axisymmetric motion. In the zerofrequency limit, the self-mobility correction near a hard sphere is recoveredonly if the membrane has a non-vanishing resistance towards shearing. Wefurther compute the particle in-plane mean-square displacement of a nearbydiffusing particle, finding that the membrane induces a long-lastingsubdiffusive regime. Considering capsule motion, we find that the correction tothe pair-mobility function is solely determined by membrane shearingproperties. Our analytical calculations are compared and validated with fullyresolved boundary integral simulations where a very good agreement is obtained.

Hydrodynamic mobility of a solid particle nearby a spherical elastic membrane. II. Asymmetric motion