The quality register in PRINCE2 is used to record all planned quality activities, such as quality checks and audits, which determine whether the project's products are fit for purpose. It serves as a log of the quality activities conducted and their outcomes, ensuring quality control throughout the project. References:
PRINCE2 Foundation Handbook, Quality Register section.

In the 'Managing Product Delivery' process of PRINCE2, the team manager's perspective is considered by ensuring that work packages provided by the Project Manager are agreed upon by the Team Manager. This agreement includes understanding the requirements, scope, and criteria of the work packages, thus ensuring that the team manager is fully informed and agrees with what needs to be delivered.References: PRINCE2 Foundation Manual

The project board reviews the Project Initiation Documentation (PID) during an end stage assessment primarily to review summarized progress to date and to decide the future course of action for the project. This review helps determine whether the project is still viable and if the project should continue into its next stage based on performance against the plan and the business case.References: PRINCE2 Foundation Manual

In PRINCE2, a project's benefits are defined as the measurable improvements that result from the outcomes achieved through the use of the project's outputs. These benefits should align with the objectives set out in the business case and are an essential part of the project's value proposition. References: PRINCE2 Foundation Training Manual; PRINCE2 2017 Foundation handbook.

During the 'Initiating a Project' process in PRINCE2, a detailed plan for the work needed for project initiation is established. This includes developing the various management strategies and the project initiation documentation (PID) that will guide the project's execution and control phases.References: PRINCE2 Foundation Manual