  The exact solution of a system of bilinear identities derived in the first
part of our work [Nucl.Phys.A 938 (2015) 59] for the case of real Grassmann-odd
tensor aggregate of the type $(S,V_{\mu},\!\,^{\ast}T_{\mu \nu},A_{\mu}, P)$ is
obtained. The consistency of the solution with a corresponding system of
bilinear identities including both the tensor variables and their derivatives
$(\dot{S},\dot{V}_{\mu},\!\,^{\ast}\dot{T}_{\mu\nu},\dot{A}_{\mu},\dot{P})$ is
considered. The alternative approach in solving of the algebraic system based
on introducing complex tensor quantities is discussed. This solution is used in
constructing the mapping of the interaction terms of spinning particle with a
background (Majorana) fermion field $\Psi^{i}_{{\rm
M}\hspace{0.02cm}\alpha}(x)$. A way of the extension of the obtained results
for the case of the Dirac spinors $(\psi_{{\rm
D}\hspace{0.03cm}\alpha},\theta_{{\rm D}\hspace{0.03cm}\alpha})$ and a
background Dirac field $\Psi^{i}_{{\rm D}\hspace{0.03cm}\alpha}(x)$, is
suggested. It is shown that for the construction of one-to-one correspondence
between the most general spinors and the tensor variables, we need a four-fold
increase of the number of the tensor ones. A connection with the higher-order
derivative Lagrangians for a point particle and in particular, with the
Lagrangian suggested by A.M. Polyakov, is proposed.
