We report the chemical composition of organic molecules in fragment B of comet 73P/Schwassmann-Wachmann 3 (SW3). Comet SW3 is a Jupiter-family comet that split into three fragments during its 1995 apparition and later into additional components. It was expected that fresh ices from deep within the presplit nucleus were exposed on the surface of each fragment. We observed SW3 with the Subaru telescope in 2006 early May when component B was disintegrating rapidly. If this exposed fresh ices from deeper layers of the original nucleus, mixing ratios obtained from our observations may reflect the pristine nature of the comet. Based on our results, comet SW3-B was depleted in C₂H₆ and C₂H ₂ with respect to most comets from the Oort Cloud reservoir, suggesting its formation region might have differed from that of the dominant Oort Cloud comets. Furthermore, the chemical composition of SW3-B was similar to that of SW3-C, suggesting that the presplit nucleus was almost homogeneous in volatile composition. The combined results demonstrate that depleted-organics comets from a common formation zone entered both reservoirs, of Jupiter-family comets and and Oort Cloud comets, but likely in different fractions.