What is the significance of Fortinbras having the last line in Hamlet?

Shakespeare wanted to establish that Hamlet had not been insane or culpable in any way in the deaths of Laertes, Gertrude, and Claudius that had just taken place, or in the deaths of Polonius, Ophelia, Rosencrantz and Guildenstern which had occurred before. There were only two characters left alive who could speak the last lines, Horatio and Fortinbras. Horatio was the only one who knew all the facts from the time the ghost appeared in the first act right up until the final scene, and he promised that he would tell the whole story in good time. But it would have been inappropriate for him to try to do that at the very end of the play because there would have been far too much to tell--and anyway, the audience already knows these facts after sitting through an exceptionally long and complicated play. So Fortinbras was used to verify that Hamlet died with honor and dignity, leaving the audience with the assurance that Hamlet's reputation would be unblemished and a feeling of closure. It was also appropriate that Fortinbras should speak the closing words, since it was probable that, with Hamlet's nomination, he was likely to become King of Denmark. His words, therefore, would carry the most weight with those in attendance. His closing words are:

Let four captains
Bear Hamlet like a soldier to the stage;
For he was likely, had he been put on,
To have proved most royal; and, for his passage,
The soldiers' music and the rites of war
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.

Horatio could not close the play with such authority, since he is not of royal blood, is really only a poor student, and was just a friend and confidant of the dead Prince. Shakespeare does something very similar in Julius Caesar. Mark Antony ia a far more important character than Octavius, but Shakespeare has Octavius speak the closing lines about Brutus because Octavius, as Julius Caesar's nephew and heir, is the more distinguished character and is destined to become Emperor. Antony praises the dead Brutus as the only truly honorable member of the conspirators, and then Octavius speaks the closing lines of the play:

According to his virtue let us use him
With all respect and rites of burial.
Within my tent his bones tonight shall lie,
Most like a soldier, order'd honorably.
So call the field to rest, and let's away,
To part the glories of this happy day.