If an employee is funded by multiple chartstrings managed by more than one department, who initiates the Direct Retro transaction?

The department that owns the position (rather than the department that owns the funding).

For example, if an employee works primarily for department A and their position is funded by department A and partially by department C, department A would initiate the Direct Retro and enter the chartstrings for both departments A and C. If approval is required from department C, department A can attach approval documentation to the Direct Retro transaction.