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The exact solution of a system of bilinear identities derived in the firstpart of our work [Nucl.Phys.A 938 (2015) 59] for the case of real Grassmann-oddtensor aggregate of the type $(S,V_{\mu},\!\,^{\ast}T_{\mu \nu},A_{\mu}, P)$ isobtained. The consistency of the solution with a corresponding system ofbilinear identities including both the tensor variables and their derivatives$(\dot{S},\dot{V}_{\mu},\!\,^{\ast}\dot{T}_{\mu\nu},\dot{A}_{\mu},\dot{P})$ isconsidered. The alternative approach in solving of the algebraic system basedon introducing complex tensor quantities is discussed. This solution is used inconstructing the mapping of the interaction terms of spinning particle with abackground (Majorana) fermion field $\Psi^{i}_{{\rmM}\hspace{0.02cm}\alpha}(x)$. A way of the extension of the obtained resultsfor the case of the Dirac spinors $(\psi_{{\rmD}\hspace{0.03cm}\alpha},\theta_{{\rm D}\hspace{0.03cm}\alpha})$ and abackground Dirac field $\Psi^{i}_{{\rm D}\hspace{0.03cm}\alpha}(x)$, issuggested. It is shown that for the construction of one-to-one correspondencebetween the most general spinors and the tensor variables, we need a four-foldincrease of the number of the tensor ones. A connection with the higher-orderderivative Lagrangians for a point particle and in particular, with theLagrangian suggested by A.M. Polyakov, is proposed.

Mapping between the classical and pseudoclassical models of a relativistic spinning particle in external bosonic and fermionic fields. II