There need be no information transferred.

I didn't quite follow this. From where to where?

But anyway, yes, that's correct that the referents of the two claims aren't the same. This could stand some further clarification as to why. In fact, Descendant's claim makes a direct reference to the individual who uttered it at the moment it's uttered, but Ancestor's claim is not about himself in the same way. As you say, he's attempting to refer to all of his descendants, and on that basis claim identity with whichever particular one of them happens to win the lottery, or not, as the case may be. (As I note above, this is not your usual equivalence relation.) This is an opaque context, and Ancestor's claim fails to refer to a particular individual (and not just because that individual exists only in the future). He can only make a conditional statement: given that X is whoever it is will win the lottery (or not), the probability that person will win the lottery (or not) is trivial. He lacks something that allows him to refer to Descendant outside the scope of the quantifier. Descendant does not lack this, he has what Ancestor did not have-- the wherewithal to refer to himself as a definite individual, because he is that individual at the time of the reference.

But a puzzle remains. On this account, Ancestor has no credence that Descendant will win the lottery, because he doesn't have the means to correctly formulate the proposition in which he is to assert a credence, except from inside the scope of a universal quantifier. Descendant does have the means, can formulate the proposition (a de se proposition), and can now assert a credence in it based on his understanding of his situation with respect to the facts he knows. And the puzzle is, Descendant's epistemic state is certainly different from Ancestor's, but it seems it didn't happen through Bayesian updating. Meanwhile, there is an event that Descendant witnessed that served to narrow the set of possible worlds he situates himself in (namely, that he is now numerically distinct from any of the other descendants), but, so the argument goes, this doesn't count as any kind of evidence of anything. It seems to me the basis for requiring diachronic consistency is in trouble.