The ship of Theseus paradox John made an important point that seldom comes up in this debate. Its also important to note that the original version of this example did not include Ship B. That was added way later in history, around Kant's time if I'm not mistaken. However, when the Greek's posed this question it was in the pre-Cartesian sense of identification. And in the sense of identification, a possession require agency, thus Theseus' ship is always the one captained by Theseus & his crew.
But in the later examples, Theseus is long since passed on, therefore is Ship A or Ship B Theseus' Ship. Semantics is important here, because the words we use necessarily condition our view of the situation. In this case, once Theseus' ORIGINAL ship is torn apart, neither are Theseus' Ship anymore. Ship A is a new ship that takes up the same point in space/time that occupies the point that was once occupied by Theseus' ship. Ship B is a 'reconstructed' sum of the parts of Theseus' original ship.
Not sure if anyone is feeling those answers, but that is a possible outlook after having addressed this problem through multiple lenses and looking for different aspefts embedded in the argument.