The project manager is a specialist consultant that represents the client and protects their interests, assuming responsibility for the day-to-day management of the project and long term achievement of the client's objectives.
Experienced and confident clients may wish to run much of the project themselves but still welcome specialised technical support/ knowledge from their PM plus the skills of an industry-specific cost consultant.
Other clients simply lack sufficient time, resource, confidence or technical skills to take on the full time responsibility of organising and driving an onerous relocation project entirely themselves – this is where the consultant steps in, purely for the duration of the project - your "imported" expert.
The PM should be entirely independent so as to avoid any conflict of interest. They can be part of a large multinational firm, aligned to the commercial agent, or conversely a small boutique completely independent organisation. The choice of PM is entirely down to the client and the type of chemistry/ service level they desire.
The PM should operate as if part of the client organisation, sitting firmly client-side of the table, with the ability to make judgements, issue instructions and review progress on behalf of the client. As such, this role frees up clients to continue with their "day job", undistracted.