The project manager should request the high-performing team member to mentor the other team members.
This is because mentoring is a way of recognizing and rewarding the team member's expertise and contributions, as well as enhancing the skills and performance of the other team members. Mentoring can also foster a positive team culture, increase collaboration and trust, and reduce turnover and attrition. The project manager should also provide feedback and appreciation to the high-performing team member, and ensure that the mentoring process is aligned with the project objectives and expectations. The other options are not as effective or appropriate as requesting the high-performing team member to mentor the other team members.
Promoting the higher performing team member to a higher position may not be feasible or desirable, as it may create resentment among the other team members, disrupt the team dynamics, or reduce the team member's motivation and satisfaction. Reminding the high-performing team member to focus on shared rewards rather than individual rewards may be perceived as unfair or discouraging, as it may imply that the team member's efforts are not valued or appreciated. Rewarding the high-performing team member privately to avoid team disruption may also be seen as unfair or secretive, as it may create a sense of favoritism or inequality among the team members, and undermine the team morale and cohesion. References: PMBOK Guide, 6th edition, Chapter 9.4.2, 9.4.3, The Benefits of Mentoring in Project Management - PMI