Working memory (WM) content is mostly stored in neurons preferring contralateral cues in bilateral prefrontal cortex (PFC) [2], but can travel between hemispheres [3]. This is thought to support full-field spatial WM continuity. Recently, temporal continuity in WM has been linked to activity-silent mechanisms in PFC supporting behavioral serial dependence (SD) between successive trials [1]. Moreover, SD increases when prefrontal activity-silent traces of previous memories are reactivated in the fixation period by either internal or external (e.g. transcranial magnetic stimulation, TMS) inputs [1]. How memory traces and reactivations interact with anatomical lateralization to ensure both WM spatial and temporal continuity is currently unknown. Here, we asked if SD is lateralized and how its mechanisms are propagated between hemispheres. We tested the lateralization of SD using human and monkey behavioral responses and TMS experiments in humans, and we analyzed simultaneous bilateral PFC multiunit recordings in one monkey performing a spatial WM task to assess interhemispheric transfer of fixation-period reactivations. We found that SD for successive stimuli presented across hemifields was diminished compared to within-hemifield sequential stimuli. Furthermore, unilateral TMS in humans showed increased SD for fixation-period TMS pulses in the hemisphere when both stimuli were contralateral to the memorandum, but not for ipsilateral stimuli. This indicates that reactivations of memory traces are constrained to one hemisphere. We then tested the coordination of neural representations across hemispheres. Locations decoded from the two hemispheres were strongly correlated during the delay but uncorrelated during reactivations, consistent with private reactivations of serial memory traces within each hemisphere. This shows an incomplete spatial continuity of SD in WM. Future computational work will gain understanding on how lateralized activity-silent mechanisms can give rise to this pattern of SD effects, and their implications for combined temporal and spatial continuity in WM.