The two generals have to be in the same stack (doesn't matter if it's in a city or in the field) and ancillaries can be swapped between any general; FM's, recruited and bribed ones.
I never tried it, but swapping ancillaries between agents in the same stack might also work, I don't know.

Anyway. It should work as long as the recipient does not allready have an ancillary that excludes the one you're trying to switch.
For instance, if the general already has the chirurgeon, he can no longer get an extra docter or physician. Or if your FM starts out with a clerk, he can't get a spear carrier.
You can check for yourself what ancillaries are mutually exclusive by opening up export_descr_ancillaries.txt and look for "ExcludedAncillaries".

You do the actual swapping by clicking on the picture of the ancillary and draging it to the portrait of the recieving character.

Off topicy; isn't this feature either removed or broken in Empire: Total War?