During the Managing a Stage Boundary process, the Stage Plan for the next stage is created and submitted for approval. This plan outlines the work to be done in the upcoming stage and is a critical element for Project Board review before the next stage can commence. References: PRINCE2Foundation Training Manual; PRINCE22017 Foundation handbook.

The Benefits Management Approach in PRINCE2 is designed to outline how and when the improvements (benefits) delivered by the project will be measured and to define the reason for delivering these improvements. This approach ensures that there is a clear understanding of the project's intended outcomes and how these will contribute to the organization's objectives, thereby justifying the project's existence and ongoing investment.
PRINCE2 Foundation Manual

The Communication Management Approach in PRINCE2 outlines the means and frequency of communication to stakeholders throughout the project. This document specifies how often stakeholders require updates and information regarding the project's progress and any issues that arise, ensuring that all parties are adequately informed. References: PRINCE2 7 Foundation Handbook and official training materials.

Maintaining the business case during the project lifecycle involves regularly updating it to reflect changes and actual experiences such as incurred costs. This ensures that the project remains viable and aligned with business objectives, as part of the continual justification process. The business case is dynamically managed to reflect any changes in the project's environment and is a fundamental part of the 'business case theme' in PRINCE2.
PRINCE2 7 Foundation source documents on business case management.

The purpose of the Directing a Project process in PRINCE2 is to enable the Project Board to exercise overall control over the project while delegating day-to-day management of the project stages to the Project Manager.
This ensures that the Project Board can make key decisions and remain accountable for the project's success while not being involved in the lower-level, day-to-day activities. References: PRINCE2 Foundation manual, PRINCE2 official resources