Thanks!!
Also, thanks to your help, I realized that it needs to change the ParentFleetID to match the ownership fleet.
So there are three things to be changed:
FCT_Fleet - ParentFleetID
FCT_Fleet - RaceID
FCT_Ship - RaceID
As bonus track, you should also need the Assigned Pop ID (so it will appears in the planet you want)
With that things changed the ship appears in the new empire