According to the PMBOK Guide, risk prioritization is the process of assigning a level of importance to each identified risk based on its probability and impact, as well as other factors such as urgency, stakeholder tolerance, and project objectives.
Risk prioritization helps the project team to focus on the most significant risks and allocate resources accordingly. One of the tools and techniques for risk prioritization is stakeholder engagement, which involves involving the key stakeholders in the risk analysis and decision making process.
Stakeholder engagement helps to ensure that the risk prioritization reflects the expectations and preferences of the stakeholders, and that they are aware of and agree with the results.
By engaging the key stakeholders during the prioritization process, the risk manager could have avoided the board's request to sort the risks differently, as the board would have been part of the process and would have accepted the outcome.
References: = PMBOK Guide, 6th edition, pages 406-407; The Standard for Risk Management in Portfolios, Programs, and Projects, page 67.