  We pursue our investigations, initiated in [8], about stochastic integration
with respect to the non-commutative fractional Brownian motion (NC-fBm). Our
main objective in this paper is to compare the pathwise constructions of [8]
with a Skorohod-type interpretation of the integral. As a first step, we
provide details on the basic tools and properties associated with
non-commutative Malliavin calculus, by mimicking the presentation of Nualart's
celebrated treatise [14]. Then we check that, just as in the classical
(commutative) situation, Skorohod integration can indeed be considered in the
presence of the NC-fBm, at least for a Hurst index H > 1 4.This finally puts us
in a position to state and prove the desired comparison result, which can be
regarded as an It{\^o}-Stratonovich correction formula for the NC-fBm.
