There's even a theory which says that Serge and Lynx never swapped bodies, but rather that it was their memories which were swapped. Lynx is still Lynx but acts as Serge (this would explain why Harle in the Dimensional Vortex claims that Lynx is indeed still Lynx), and Serge is still Serge but acts as Lynx (for FATE, it makes no difference as long as she has an agent to carry out her plan).
That's a theory which isn't mine and was posted a long time ago. I don't really know if it is really plausible.