We report the first measurements of spin injection in to graphene through a 20 nm thick tungsten disulphide (WS$_2$) layer, along with a modified spin relaxation time ({tau}s) in graphene in the WS$_2$ environment, via spin-valve and Hanle spin-precession measurements, respectively. First, during the spin-injection into graphene through a WS$_2$-graphene interface, we can tune the interface resistance at different current bias and modify the spin injection efficiency, in a correlation with the conductivity-mismatch theory. Temperature assisted tunneling is identified as a dominant mechanism for the charge transport across the interface. Second, we measure the spin transport in graphene, underneath the WS$_2$ crystal and observe a significant reduction in the {tau}s down to 17 ps in graphene in the WS$_2$ covered region, compared to that in its pristine state. The reduced {tau}s indicates the WS$_2$-proximity induced additional dephasing of the spins in graphene.
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