During the Managing a Stage Boundary process, the Business Case is used to justify the continuing viability of the project. This involves reviewing and, if necessary, updating the Business Case to reflect any changes or new insights that might impact the project's justification. This helps the Project Board make informed decisions about the future progression of the project.
PRINCE2 7 Foundation handbook and official documents.

The project board in PRINCE2 represents the three project interests, which are business (value for money), user (those who will use the project's outputs), and supplier (those who provide the resources and skills). The project board is responsible for overseeing the project, ensuring that it delivers value and meets the requirements set out by these three interest groups. References: PRINCE2 Foundation Handbook, Project Board section.

To control the size of the Project Board on a project that involves multiple users and suppliers, creating user and supplier groups is an effective strategy. These groups can represent broader interests and provide input to the Project Board, helping to streamline decision-making processes without overloading the board with members. References: PRINCE2 Foundation manual, PRINCE2 official resources

A PRINCE2 project must demonstrate the application of its seven principles throughout the project's lifecycle.
These principles are universal, self-validating, and empowering, ensuring that the project management approach is effective and applicable under various project circumstances. References: PRINCE2 Foundation Handbook, Principles section.

The purposes of the quality theme in PRINCE2 are to establish how the project will ensure that products are fit for purpose and meet stakeholder expectations (purpose 2) and to ensure that the project's objectives are desirable and achievable, which pertains to ensuring that the project has a solid business justification (purpose
3). References: PRINCE2 Foundation Handbook, Quality Theme section.