Invoice a director of a limited company.

A customer will not contract with the company but instead wants to contract with the director directly so the services cannot be delegated to another director or employee.

Can the company invoice the director to get this money into the company (take advantage of losses b/fwd etc) and what should the invoice say? How would HMRC view this? Would they say the work was carried out personally by the director, and invoiced in the name of the director and therefore they are self-employed, as it looks to me that they would just say this was done to avoid Class 4 and take advantage of no additional tax on dividends.

Thank you for your help.