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Van der Waals heterostructures consisting of 2D semiconductors and conjugated molecules are of increasing interest because of the prospect of a synergistic enhancement of (opto)electronic properties. In particular, perylenetetracarboxylic dianhydride (PTCDA) on monolayer (ML)‐MoS2 has been identified as promising candidate and a staggered type‐II energy level alignment and excited state interfacial charge transfer have been proposed. In contrast, it is here found with inverse and direct angle resolved photoelectron spectroscopy that PTCDA/ML‐MoS2 supported by insulating sapphire exhibits a straddling type‐I level alignment, with PTCDA having the wider energy gap. Photoluminescence (PL) and sub‐picosecond transient absorption measurements reveal that resonance energy transfer, i.e., electron–hole pair (exciton) transfer, from PTCDA to ML‐MoS2 occurs on a sub‐picosecond time scale. This gives rise to an enhanced PL yield from ML‐MoS2 in the heterostructure and an according overall modulation of the photoresponse. These results underpin the importance of a precise knowledge of the interfacial electronic structure in order to understand excited state dynamics and to devise reliable design strategies for optimized optoelectronic functionality in van der Waals heterostructures. [ABSTRACT FROM AUTHOR]