The major Dutch, French and British international concerns, as well as Exxon-Mobil and probably Chevron, of course are the most qualified to rebuild and strengthen the Iraqi oil programs.
These companies have the expertise, and the large numbers of trained geologists, engineers, technicians and supply specialists needed to expand and manage the fields, construct modern onsite refineries and get the hydrocarbons into the pipeline and tanker chain- as well as train Iraqis as professionals and managers, now that increasing numbers of Iraqi students are once again receiving technical education.

Of course the other possibility is Lukoil, the Russian giant who had negotiated contracts with Saddam Hussein's government, possibly in cooperation with China. Now would that be preferable?
They probably will get a piece of the action, but will not control the development.

Before and during Saddam Hussein' rule, Iraqi personnel were trained in American and British universities, but these people have retired, died, or moved out of the country. Iraqi students studying in fields related to hydrocarbon production and transportation are again at American and Canadian Universities, as well as the University center in Qatar and elsewhere, but it is too soon for them to be an important factor in guiding their petroleum industry.