In a situation where the project team members lack the necessary technical skills for project success, it's crucial for the project manager to take proactive steps to bridge this skill gap. This could involve finding and providing relevant training to the team members. This approach ensures that the team has the necessary competencies to deliver on the project's objectives, even when the customer's requirements are unclear or changing. It's also aligned with the principles of hybrid project management, which emphasize flexibility, continuous learning, and adaptability in the face of change. References: PMBOK Guide - Sixth Edition, Section 9.4 Manage Project Team, pg. 349; Section 9.5 Control Resources, pg. 356.

Agile promotes continuous improvement and collaboration. However, if a new process affects key stakeholders outside the development team (in this case, the business), then alignment is required. The project manager should engage the business manager and discuss the proposed approach and its benefits to secure approval.
The Agile Practice Guide supports direct stakeholder engagement when process changes affect external contributors or consumers of deliverables. Agility includes openness to improvement, but also emphasizes communication and stakeholder buy-in.
Option B (PMO) may help, but the business manager is the decision-maker.
Option C delays potential value.
Option D ignores required alignment with business stakeholders.
References:
Agile Practice Guide, Chapter 3 - Tailoring and Stakeholder Collaboration PMBOK Guide - Seventh Edition, Stakeholder Performance Domain
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According to project management best practices, a change request is a formal document that describes the proposed changes to a project and the impact they will have on the project scope, schedule, budget, quality, and risks12. A change request should be initiated by the party that is requesting the change, not by the party that is delivering the project3. Therefore, the receiving manager should be responsible for issuing a change request to the project manager, who can then evaluate it and approve or reject it.
Delivering the project to the receiving manager on time, without ensuring that they are ready to accept it, could lead to poor knowledge transfer, lack of ownership, and increased risks of errors or defects4. Informing the project sponsor of the delay and replanning the activities could be done after the change request is approved, but not before. Issuing an internal change request to secure the resources for an additional two weeks could be seen as a unilateral decision by the project manager, without considering the needs and expectations of the receiving organization.
Therefore, the most appropriate and professional action for the project manager to do is to request that the receiving manager issue a change request to prolong the project by two weeks, and then follow the change management process to handle it. This way, the project manager can ensure that the project is delivered in accordance with the agreed scope, quality, and stakeholder satisfaction.

The departure of a key project resource can pose a significant risk to the continuity and success of a project.
To mitigate this risk, establishing a proactive knowledge-sharing plan is essential. This involves creating a structured approach to capture the departing resource's knowledge and expertise, which can then be transferred to the remaining team members. This ensures that critical project information and skills are retained within the team, minimizing the impact of the resource's departure. A knowledge-sharing plan can include documentation of processes, training sessions, and mentoring programs12.
References:
PMBOK Guide, 6th Edition, Section 9.1.3.1: Plan Resource Management
PMI's Practice Standard for Project Risk Management
How to Mitigate Resource Risk in Project Management? - Resources Library PMP Exam Strategies for Risk Response: Mitigate Risk, Avoid, or Transfer