To gain the support of an influential stakeholder who is skeptical about the value of project management processes, the project manager should clarify the project roles and responsibilities and share the purpose of the project management processes. This approach helps in aligning the stakeholder's understanding with the project objectives and demonstrates how the processes add value to the project's success. Engaging the stakeholder in this manner is more likely to result in their buy-in and support, as it addresses their concerns directly and shows a willingness to collaborate and communicate effectively12345.
References: The approach of clarifying roles and sharing the purpose is supported by PMI's guidelines on stakeholder engagement and is consistent with best practices in project management and business analysis12345678.