  We demonstrate enhanced robustness of the supercurrent through graphene-based
Josephson junctions in which strong spin-orbit interactions (SOIs) are induced.
We compare the persistence of a supercurrent at high magnetic fields between
Josephson junctions with graphene on hexagonal boron-nitride and graphene on
WS$_2$, where strong SOIs are induced via the proximity effect. We find that in
the shortest junctions both systems display signatures of induced
superconductivity, characterized by a suppressed differential resistance at a
low current, in magnetic fields up to 1 T. In longer junctions however, only
graphene on WS$_2$ exhibits induced superconductivity features in such high
magnetic fields, and they even persist up to 7 T. We argue that these robust
superconducting signatures arise from quasi-ballistic edge states stabilized by
the strong SOIs induced in graphene by WS$_2$.
