From an RP standpoint, unless the player defined, or is willing to define the player's family, it is not a fun thing for many GM's to have to define a character's family. Many characters are conveniently devoid of familial ties.
Besides, in most monarchies, the family has to petition the crown for inheritance. I can see local properties following local laws, but clearly "imperial level assets" logically should be covered under imperial level rules. Since, according to TTB, imperial government begins at the subsector duchy, that would be the relevant default heir.
Now, I'd forgotten the Al-Morai bits, and that gives me the idea that the Duke is the one to "normalize" and "enact by letters patent" or "enact by these presents" (herald for "make real in accord with law and custom") the actual corporation of the ship, based upon ship's records.
This provides for both the family interaction (the family wants the dead guy's share), and roleplay with the duke, explaining the contracts, the shares, and having the players codify what they have been doing. Then have the Duke, based upon what they've said, incorporate them under letters patent, adding his 1% payable annually... and of course also the Emperor's 1%, and maybe the sector and domain ducal 1% shares, too.
It also provides opportunities for players to induce changes by subtle deceptions... and possibly also to ask the Duke for changes overtly.
Or, if the players have "odd legal history," a chance for the duke to demand extraordinary actions to justify extraordinary rewards... "Y'see, I've this little problem, and judging from your IMoJ files, you do wetwork... Here's my problem: Baron Schlubnutzen; cure it, and get your ship back. You've 3 months.... and 6 passage coupons each."
