  The purpose of this paper is to extend the construction of the PSS-type
isomorphism between the Floer homology and the quantum homology of a monotone
Lagrangian submanifold $L$ of a symplectic manifold $M$, provided that the
minimal Maslov number of $L$ is at least two, to arbitrary coefficients. We
provide a proof, again over arbitrary coefficients, that this isomorphism
respects the natural algebraic structures on both sides, such as the quantum
product and the quantum module action. This isomorphism serves as the technical
foundation for the construction of Lagrangian spectral invariants in a joint
paper with Remi Leclercq (arXiv:1505:07430). Our constructions work when the
second Stiefel--Whitney class of $L$ vanishes on the image of the boundary
homomorphism $\pi_3(M,L) \to \pi_2(L)$, a condition strictly weaker than being
relatively Pin; in particular we do not require $L$ to be orientable. The
constructions are done using canonical orientations, and require no further
choices such as relative Pin-structures. Such structures do however play a
significant role when endowing the various complexes and homologies with
structures of modules over Novikov rings, and in calculations.
