The analysis of the relation between modular P$_1$CT-symmetry -- a
consequence of the Unruh effect -- and Pauli's spin-statistics relation is
continued. The result in the predecessor to this article is extended to the
Lorentz symmetric situation. A model $\G_L$ of the universal covering
$\widetilde{L_+^\uparrow}\cong SL(2,\complex)$ of the restricted Lorentz group
$L_+^\uparrow$ is modelled as a reflection group at the classical level. Based
on this picture, a representation of $\G_L$ is constructed from pairs of
modular P$_1$CT-conjugations, and this representation can easily be verified to
satisfy the spin-statistics relation.