Nothing. It belongs to you, not the fleet.

iI believe you cannot use the special fleet hull materials if your not in a fleet though.

The difference? One is a fleet ship, the other is a C-Store ship with a console.
Fact: My Tactical Escort Retrofit has a cloaking device... The Fleet Tactical Escort Retrofit does not.

krayuskorianis the real question than is now that you have the Cloaking Device can it go in the new ship?

I know the Tactical Escort Retrofit and Gal X are the only ones able to use a Cloaking Device, but will that expand to include the Fleet Tactical Escort Retrofit?

Yes, it was said in the Priority One interview.

You can move a console from a C-Store ship to its Fleet equivalent, i.e. take the Cloaking Device from the Tactical Escort Retrofit and put it in the Fleet Tactical Escort Retrofit, thereby gaining both the special power and the boosted hull HP and extra console slot.

So really, the C-Store ship has no advantage over the Fleet variant. If you've already bought it, you're gaining nothing by flying it instead of the Fleet version, which strikes me as incredibly dumb. C-Store ships should really be buffed to match Fleet ships. Fleet ships, on the other hand, allow a greater variety of ships one can fly; endgame Nova-class, or Hope-class, or non-cloaking Tactical Escort Retrofits, or whatever. That honestly seems very fair to me.

Is this confirmed?

Yes, I have a Fleet Tactical Escort Retrofit and i have put the cloaking console on it from my cstore ship.