The discovery of the electrons' chiral induced spin selective transmission (CISS) through chiral molecules has opened the pathway for manipulating spin transport in nonmagnetic structures on the nanoscale. CISS has predominantly been explored in structurally helical molecules on surfaces, where the spin selectivity affects only the spin polarization of the electrons along their direction of propagation. Here, we demonstrate a spin selective electron transmission for the point-chiral molecule 3-methylcyclohexanone (3-MCHO) adsorbed on the chiral Cu(643)R surface. Using spin- and momentum-resolved photoelectron spectroscopy, we detect a spin-dependent electron transmission through a single layer of 3-MCHO molecules that depends on all three components of the electrons' spin. Crucially, exchanging the enantiomers alters the electrons' spin component oriented parallel to the terraces of the Cu(643)R surface. The findings are attributed to the enantiomer-specific adsorption configuration on the surface. This opens the intriguing opportunity to selectively tune CISS by the enantiospecific molecule-surface interaction in all-chiral heterostructures.