Reference:
http://prince2.wiki/Continued_business_justification

The risk response type that is applied on a pain/gain basis is 'Share'. Sharing involves partnering with others to share the impact of the risk. This is often used for both threats and opportunities where sharing the risk can enhance the capability to capitalize on the opportunity or mitigate the threat, with potential gains or savings being distributed according to an agreed formula.References: PRINCE2 7 Foundation handbook and documents.

In the 'risk management' technique within PRINCE2, considering the organization's environment is essential during the 'Identify' step. This phase involves understanding the context in which the project operates, including external and internal factors that could affect the project. This context is crucial for identifying potential risks that could impact the project's objectives.References: PRINCE2 7 Foundation resources on risk management technique.

The purpose of the Risk theme in PRINCE2 is to establish a cost-effective procedure to identify, assess, and control uncertainties or risks. This ensures that the project can cope with risks effectively. The Risk theme supports decision-making by improving the understanding of risks and their likely impact on achieving the project's objectives.
PRINCE2 7 Foundation resources and study materials.

The Communication Management Strategy is used in PRINCE2 to maintain a record of stakeholders who have an interest in the project and their information requirements. This document outlines how and when stakeholders will be kept informed about the project's progress and any issues that may arise. References:
PRINCE2 Foundation manual, PRINCE2 official resources