Question

fortinbras: let us haste to hear it,
and call the noblest to the audience.
for me, with sorrow i embrace my fortune;
i have some rights of memory in this kingdom,
which now to claim my vantage doth invite me. (340)
horatio: of that i shall have also cause to speak,
and from his mouth whose voice will draw on more:
but let this same be presently perform’d,
even while men’s minds are wild, lest more mischance
on plots and errors happen. (345)
fortinbras: let four captains
bear hamlet, like a soldier, to the stage;
for he was likely, had he been put on,
to have prov’d most royally: and, for his passage,
the soldiers’ music and the rites of war (350)
speak loudly for him.
take up the bodies: such a sight as this
becomes the field, but here shows much amiss.
go, bid the soldiers shoot. a dead march. exeunt, bearing off the bodies; after which a peal of ordnance is shot off.
now that claudius and hamlet have died, who will become the next king of denmark?
horatio fortinbras rosencrantz laertes

Explanation:

From the text, Fortinbras says he has "some rights of memory in this kingdom" and "to claim my vantage doth invite me". Also, he orders the soldiers and makes arrangements related to the succession context (after Claudius and Hamlet's deaths), indicating he will be the next king. Horatio is a friend of Hamlet, Rosencrantz is a courtier (and already involved in the plot earlier), Laertes died in the final duel, so Fortinbras is the one to take the throne.

Answer:

B. Fortinbras