Context. Classical hot cores are rich in molecular emission, and they show a high abundance of complex organic molecules (COMs). The emergence of molecular complexity that is represented by COMs, in particular, is poorly constrained in the early evolution of hot cores. Aims: We put observational constraints on the physical location of COMs in a resolved high-mass protostellar envelope associated with the G328.2551-0.5321 clump. The protostar is single down to ~400 au scales and we resolved the envelope structure down to this scale. Methods: High angular resolution observations using the Atacama Large Millimeter Array allowed us to resolve the structure of the inner envelope and pin down the emission region of COMs. We use local thermodynamic equilibrium modelling of the available 7.5 GHz bandwidth around ~345 GHz to identify the COMs towards two accretion shocks and a selected position representing the bulk emission of the inner envelope. We quantitatively discuss the derived molecular column densities and abundances towards these positions, and use our line identification to qualitatively compare this to the emission of COMs seen towards the central position, corresponding to the protostar and its accretion disk. Results: We detect emission from 10 COMs, and identify a line of deuterated water (HDO). In addition to methanol (CH3OH), methyl formate (CH3OCHO) and formamide (HC(O)NH2) have the most extended emission. Together with HDO, these molecules are found to be associated with both the accretion shocks and the inner envelope, which has a moderate temperature of Tkin ~ 110 K. We find a significant difference in the distribution of COMs. O-bearing COMs, such as ethanol, acetone, and ethylene glycol are almost exclusively found and show a higher abundance towards the accretion shocks with Tkin ~ 180 K. Whereas N-bearing COMs with a CN group, such as vinyl and ethyl cyanide peak on the central position, thus the protostar and the accretion disk. The molecular composition is similar towards the two shock positions, while it is significantly different towards the inner envelope, suggesting an increase in abundance of O-bearing COMs towards the accretion shocks. Conclusions: We present the first observational evidence for a large column density of COMs seen towards accretion shocks at the centrifugal barrier at the inner envelope. The overall molecular emission shows increased molecular abundances of COMs towards the accretion shocks compared to the inner envelope. The bulk of the gas from the inner envelope is still at a moderate temperature of Tkin ~ 110 K, and we find that the radiatively heated inner region is very compact (<1000 au). Since the molecular composition is dominated by that of the accretion shocks and the radiatively heated hot inner region is very compact, we propose this source to be a precursor to a classical, radiatively heated hot core. By imaging the physical location of HDO, we find that it is consistent with an origin within the moderately heated inner envelope, suggesting that it originates from sublimation of ice from the grain surface and its destruction in the vicinity of the heating source has not been efficient yet. A copy of the reduced datacubes is available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/cat/J/A+A/632/A57