Previous X-ray and optical studies of the galaxy cluster pair A222/223 suggested the possible presence of a filamentary structure connecting the two clusters, a result that appears to be supported by subsequent weak-lensing analyses. This filament has been reported to host a primordial warm-hot intergalactic medium, which existed prior to being heated by the interactions of the clusters. In this study, we made an attempt to examine the reported emission feature with data from an archival Suzaku observation, taking advantage of its low detector background. Because the emission is expected to be very weak, we first carefully examined all potential sources of "contamination," and then modeled the residual emission. Due to large uncertainties, unfortunately, our results can neither confirm the presence of the reported emission feature nor rule it out. We discuss the sources of uncertainties.