Large Language Models (LLMs) are likely to play a prominent role in future AI-augmented business process management systems (ABPMSs) catering functionalities across all system lifecycle stages. One such system's functionality is Situation-Aware eXplainability (SAX), which relates to generating causally sound and yet human-interpretable explanations that take into account the process context in which the explained condition occurred. In this paper, we present the SAX4BPM framework developed to generate SAX explanations. The SAX4BPM suite consists of a set of services and a central knowledge repository. The functionality of these services is to elicit the various knowledge ingredients that underlie SAX explanations. A key innovative component among these ingredients is the causal process execution view. In this work, we integrate the framework with an LLM to leverage its power to synthesize the various input ingredients for the sake of improved SAX explanations. Since the use of LLMs for SAX is also accompanied by a certain degree of doubt related to its capacity to adequately fulfill SAX along with its tendency for hallucination and lack of inherent capacity to reason, we pursued a methodological evaluation of the quality of the generated explanations. To this aim, we developed a designated scale and conducted a rigorous user study. Our findings show that the input presented to the LLMs aided with the guard-railing of its performance, yielding SAX explanations having better-perceived fidelity. This improvement is moderated by the perception of trust and curiosity. More so, this improvement comes at the cost of the perceived interpretability of the explanation.