  We use time- and angle-resolved photoemission spectroscopy (tr-ARPES) to
investigate ultrafast charge transfer in an epitaxial heterostructure made of
monolayer WS$_2$ and graphene. This heterostructure combines the benefits of a
direct gap semiconductor with strong spin-orbit coupling and strong
light-matter interaction with those of a semimetal hosting massless carriers
with extremely high mobility and long spin lifetimes. We find that, after
photoexcitation at resonance to the A-exciton in WS$_2$, the photoexcited holes
rapidly transfer into the graphene layer while the photoexcited electrons
remain in the WS$_2$ layer. The resulting charge transfer state is found to
have a lifetime of $\sim1$\,ps. We attribute our findings to differences in
scattering phase space caused by the relative alignment of WS$_2$ and graphene
bands as revealed by high resolution ARPES. In combination with spin-selective
excitation using circularly polarized light the investigated WS$_2$/graphene
heterostructure might provide a new platform for efficient optical spin
injection into graphene.
