The prefrontal cortex (PFC) is crucial for maintaining working memory across diverse cognitive tasks, yet how it adapts to varying task demands remains unclear. Compositional theories propose that cognitive processes in neural network rely on shared components that can be reused to support different behaviors. However, previous studies have suggested that working memory components are task specific, challenging this framework. Here, we revisit this question using a population-based approach. We recorded neural activity in macaque monkeys performing two spatial working memory tasks with opposing goals: one requiring movement toward previously presented spatial locations (look task) and the other requiring avoidance of those locations (no-look task). Despite differences in task demands, we found that spatial memory representations were largely conserved at the population level, with a common low-dimensional neural subspace encoding memory across both tasks. In parallel, task identity was encoded in an orthogonal subspace, providing a stable and independent representation of contextual information. These results provide neural evidence for a compositional model of working memory, where representational geometry enables the efficient and flexible reuse of mnemonic codes across behavioral contexts while maintaining an independent representation of context.