In summary, using the two-pulse coincidence photoresponse technique, we present graphene/WS2 and WS2/graphene/WSe2 photodetectors that exhibit clear signs of hot carrier injection from graphene into the van der Waals materials followed by carrier trapping. The injected hot carriers exhibit ultrafast cooling and the carrier trapping induces a long circulation of the electrons, whose combination enables an intrinsic response time of 3 ps and a responsivity of 0.26 A/W at 1560 nm. We demonstrate sub-bandgap photodetection by these heterostructures with a 3dB bandwidth of 123 MHz and a dark current eight orders of magnitude smaller than in pure graphene. Our results highlight that such heterostructures synergistically combine the ultrafast response of graphene with the high sensitivity of transition metal dichalcogenides to harvest hot carriers efficiently.