As a complex cognitive activity, knowledge transfer is mostly correlated to cognitive processes such as working memory, behavior control, and decision-making in the human brain while engineering problem-solving. It is crucial to explain how the alteration of the functional brain network occurs and how to express it, which causes the alteration of the cognitive structure of knowledge transfer. However, the neurophysiological mechanisms of knowledge transfer are rarely considered in existing studies. Thus, this study proposed functional connectivity (FC) to describe and evaluate the dynamic brain network of knowledge transfer while engineering problem-solving. In this study, we adopted the modified Wisconsin Card-Sorting Test (M-WCST) reported in the literature. The neural activation of the prefrontal cortex was continuously recorded for 31 participants using functional near-infrared spectroscopy (fNIRS). Concretely, we discussed the prior cognitive level, knowledge transfer distance, and transfer performance impacting the wavelet amplitude and wavelet phase coherence. The paired t-test results showed that the prior cognitive level and transfer distance significantly impact FC. The Pearson correlation coefficient showed that both wavelet amplitude and phase coherence are significantly correlated to the cognitive function of the prefrontal cortex. Therefore, brain FC is an available method to evaluate cognitive structure alteration in knowledge transfer. We also discussed why the dorsolateral prefrontal cortex (DLPFC) and occipital face area (OFA) distinguish themselves from the other brain areas in the M-WCST experiment. As an exploratory study in NeuroManagement, these findings may provide neurophysiological evidence about the functional brain network of knowledge transfer while engineering problem-solving.