In this article we consider the class CSL2r2c∞ 7 of non-degenerate real planar polynomial cubic vector fields, which possess two real and two complex distinct infinite singularities and invariant straight lines of total multiplicity 7, including the line at infinity. This article is a continuation of [1] in which the classification of a subfamily of this kind of systems is done in the case when the invariant affine lines form a configuration of the parallelism type (3, 3). Here we classify the subfamily of cubic systems in CSL2r2c∞ 7 , possessing configurations of invariant line of the parallelism type (3, 1, 1, 1), according to the relation of equivalence of configurations [2]. A configuration of invariant lines will be said to the of parallelism type (3, 1, 1, 1) if there exist one triplet and 3 additional lines in four distinct directions. Moreover, each invariant line, including the line at infinity of the system, is endowed with its own multiplicity and together with all the real singular points of this system located on these invariant lines, each one endowed with its own multiplicity. We denote this subfamily by CSL2r2c∞ (3,1,1,1). Our resuts are following ones: 1. We prove that there are exactly 42 distinct configurations of the type (3, 1, 1, 1). Moreover we construct all the orbit representatives of the systems in this class with respect to affine group of transformations and a time rescaling. 2. Necessary and sufficient the affine invariant conditions for the realization of each one the mentioned configurations are constructed, in terms of polynomial invariants [3], [4]. 3. Using some geometric invariants we defined we prove that all 42 configurations are realizable within the class CSL2r2c∞ (3,1,1,1) and are non-equivalent.