What to do when an internal employee transfer causes start date squabbles?

Q: “Are there any hard and fast rules covering giving notice internally if a staff member is transferring from one internal org to another? I have a “hiring” manager and an employee who want to make the transfer in two weeks, but the "releasing" manager is dragging her feet and wants to work out a schedule that could increase the amount of time up to four or more weeks. No one is happy." – Anonymous, Washington