The project manager should meet with the project team to assess their current skills and identify any gaps or training needs that may affect the project execution. This is part of the Plan Resource Management process, which involves determining the project roles, responsibilities, required skills, and reporting relationships1.
Sending the list to the project team and asking them to get training on the required skills (A) is not a proactive or effective way of managing the project resources. Asking the functional manager to review the resource pool and recommend the right individuals to join the team (B) is not feasible since the project team has already been assigned. Discussing the list with the project sponsor to confirm that the resources have the required skills is not the responsibility of the project sponsor, who is mainly concerned with the project benefits and alignment with the strategic objectives2. References:
* 1: A Guide to the Project Management Body of Knowledge (PMBOKGuide) - Seventh Edition, Chapter 8, Section 8.1.3.1
* 2: A Guide to the Project Management Body of Knowledge (PMBOKGuide) - Seventh Edition, Chapter 4, Section 4.1.2.1