Research published in the PLoS One paper "Boron Enrichment in Martian Clay" (Stephenson et al. 2013) suggest a volcanic origin for the boron, in the chemical analysis of a Martian meteorite (found in Antarctica), they explain:
A straightforward geochemical interpretation of our results is that boron, a relatively volatile and soluble element, was first concentrated in the fluid dregs of lava (4–7 ppm boron has been detected in the late stage mesostasis of other nakhlites) and then became further concentrated by any groundwater or hydrothermal fluids that came into contact with the rock.
Further modelling reported in the paper "Partitioning of light lithophile elements during basalt eruptions on Earth and application to Martian shergottites" (Edmonds, 2014), also point towards a volcanic origin. Their modelling is based on analyses of shergottite pyroxenes (Martian meteorites), stating that observed elevated boron alongside other light lithophile elements or LLE are to do with the earlier mantle chemical processes, extrapolated from those observed on Earth:
The range in LLE and trace elements observed in shergottite pyroxenes are instead consistent with concurrent mixing and fractionation of heterogeneous melts from the mantle.
Also, a volcanic origin is suggested in the Goldschmidt Conference Abstract "Boron isotopes in the nakhlites: Implications for crustal fluids on Mars" (Spivak-Berndorf et al. 2008), also based on analyses of nakhlites:
The lack of isotopic fractionation between the igneous and
secondary alteration phases in the nakhlites indicates that (1)
the B in the fluid that deposited the iddingsite was derived
from the primary igneous minerals and (2) there was minimal
B isotope fractionation between the fluid and the iddingsite