I'm of a somewhat different opinion.
The interpretation of the Almanac rule entry under ending the game seems to hinge on two key sentences:
Alpha: If you have 10 or more victory points during your turn the game ends and you are the winner! If you reach 10 points when it is not your turn, the game continues until any player (including you) has 10 points on his turn.
and
Beta: If somehow you find you have 10 victory points during another player's turn, you must wait until your next turn to claim victory.
In Alpha above, the meaning seems to support the view that indeed, the game should have ended on player A's term (per the original post/question). This seems to be Mohamad's interpretation in declaring player B's turn an "illegal" turn. Indeed, were there some neutral, omniscient 3rd party (e.g. perhaps on a webbased game), victory would be determined by proxy immediately any player has 10 points on their turn, through some basic boolean calculation. No next turn would arise and there would be no potential for this mishap or oversight to occur.
However, the reality (not hypothetical) of playing a face-to-face strategy game, is that one is responsible for declaring when one has won. e.g. The rules of Monopoly state that when a player goes around "go", they collect 200. In an automated version of the game, one's bank account may increase by 200 automatically upon passing go. However, in most competitive games, one must remember to actually claim that 200, or once the turn passes to the next player, your "right" to the 200 (per the rules) is often forfeited.
Similarly, when one buys a lottery ticket, one must choose the winning lottery numbers to win. However, while a person may take personal satisfaction from their ability to foresee winning numbers, they are not in fact rewarded for this if they fail to actually claim the winning numbers. In such a scenario, they would have picked the winning numbers (analagously, been the first to 10 points), but do not win the lottery (receive no reward for doing so) because they did not claim their win (analagously, person A did not in claim his win, and so the game did not in fact end - though, per the rules, it should have).
As a result of person A's miscalculation/oversight, the game did not in fact end. As person A seems to have handed the dice to person B and passed the turn onto B, the game in fact continued. In the absence of an omniscient, neutral, rule enforcer, the onus must be on the player to declare that they have won.
Consider the robber. If on Person X's turn, person X rolled 7, but moved the robber, but "forgot" to rob an opponent, and then passed his turn on to Person Y, it would seem that despite the rules clearly stating that when a person rolls 7 they must move the robber AND take a card from an opponent of their choice, person X through his own oversight, allowed the game to continue and therby forfeited his "right" to the card theft. Of course, if playing with lenient friends, one might expect them to allow one to fulfill that turn, however, play having moved on, there would be no obligation on the remaining players to allow him to return back to his turn and do what he should have done, per the rules, on his turn.
Similarly, by failing to bring an end to the game when he had 10 points, person A ignored the rules through his own oversight. The game should have ended - just as person X, in the example above, should have robbed a card from an opponent of his choice. In the absence of a neutral, omniscient, rule-enforcer, the onus is on each player to remember to claim his rights. By failing to end the game on his turn, person A allowed the game to continue. Person B's turn can not then be rendered illegal as a result of Person A's oversight. Similarly, if person Y (following person X's failure to rob his card) was then to use a card to buy a development card, or build a settlement etc, person X could not then say "oh wait - i forgot to rob you on my turn, so take back your settlement and let me do what I should have done on my turn, per the rules". That would require great leniency and tolerance! Person B should not be punished for Person A's oversight and consequent failure to follow the rules, and end the game on, just as Person Y can not be expected to reverse his turn to allow Person X such a great advantage that he forfeited through his own carelessness.
Having allowed the game to continue to Person B's turn, Person A finds himself now in the condition described by Beta above:
Beta: If somehow you find you have 10 victory points during another player's turn, you must wait until your next turn to claim victory.
Now certainly there are multiple ways to find yourself in this situation. (e.g. someone builds a settlement inbetween an opponent's longest route and you now have the longest routes and suddenly have 10 points!). And in some of the expansions, indeed, there are other ways to earn points out of turn. This does not change the fact that person A is also now in this situation. And the rules are clear on what Person A's options are: he must wait until his next turn.
As such, it seems person A is unfortunately, simply out of luck. The game continued as a result of his own oversight, and as such, he has no claim to the victory as although the game should have ended, in the absence of a neutral, omniscient, rule-enforcer, the onus to end the game was on him. He neglected to do so, and thus, the game did not in fact end. His turn passed, and person B declared victory. Any other conclusion would require retroactive enforcement of rules, just as person X would wish he could retroactively steal a card as he was entitled to do on his turn when he rolled a 7. Alas, such a request would require the leniency of their opponents, and such leniency can not be compelled.
Moral of the story: one needs to pay attention! Forgetfulness and inattention to detail are very costly in all strategy games and Settlers of Catan is no exception!
