Currently, T5 consoles are restricted to the specific ship they came from. This was done so there would be parity for all ships with a power throughout the game. This also allows the player to utilize this extra console slot for something besides the power if they choose.
That is very disappointing. Being able to move those consoles around would really make customization fun.
*Sigh* And they're going through with what I feared would happen... transwarp to every mission. Takes away a lot of the mystique of the game in my book, and it's to appease the new players, so that they'll stay, and buy stuff from the C-Store, and I know it.