Motivated by the synaptic tagging and capture (STC) hypothesis, it was recently shown that a weak learning, only able to produce short-term memory (STM), can succeed in establishing long-term memory (LTM) with a concomitant, stronger experience. This is consistent with the capture, by the first-tagged event, of the so-called plasticity-related proteins (PRPs) provided by the second one. Here, we describe how a concomitant session of reactivation/reconsolidation of a stronger, contextual fear conditioning (CFC) memory, allowed LTM to result from a weak spatial object recognition (wSOR) training. Consistent with an STC process, the effect was observed only during a critical time window and was dependent on the CFC reconsolidation-related protein synthesis. Retrieval by itself (without reconsolidation) did not have the same promoting effect. We also found that the inactivation of the NMDA receptor by AP5 prevented wSOR training to receive this support of CFC reconsolidation (supposedly through the production of PRPs), which may be the equivalent of blocking the setting of a learning tag in the dorsal CA1 region for that task. Furthermore, either a Water Maze reconsolidation, or a CFC extinction session, allowed the formation of wSOR-LTM. These results suggest for the first time that a reconsolidation session can promote the consolidation of a concomitant weak learning through a probable STC mechanism. These findings allow new insights concerning the influence of reconsolidation in the acquisition of memories of otherwise unrelated events during daily life situations.