Also notice that in the above verse...
Also notice that in the above verse, Allah does NOT say "a part of the knowledge of the Book" while Allah used the phrase "a part of" for the case of minister of Solomon. Some Sunnis have mentioned that the above verse refers to Abdullah Ibn Sallam, the Jewish Rabbi who converted to Islam. some other Sunnis said that it refers to all scholars of the Jews and the Christians who found the attributes of the incoming Prophet in their ancient scriptures.
The above interpretation does not seem to be correct. "The knowledge of the Book" as Quran mentions in one more place, is not as simple as recognition of the attributes of the incoming Prophet in the scripture. "The knowledge of the Book" includes the knowledge of governing rules in the Universe. As Quran stated, Asaf had only a very small part of "the Knowledge of the Book", and was able to do that extraordinary thing.
Thus this type of power has no connection with just knowing the name of an incoming prophet from a book. Furthermore, if the Sunni interpretation is correct, then it means whenever Muslims have a question, they should refer to Christians and Jews, because they have the whole knowledge of the Book while Muslims do not!
Some may argue that if the above verse is referring to Imam Ali and the rest of the twelve Imams, then what sort of evidence will this be for the unbelievers who would not accept the words of Muslims by saying the above verse to them? The answer is that the verse starts with the phrase: "And the Kuffar (unbelievers) say: You are not a messenger. Say: Sufficient as witness is..." As such, the verse is about Kuffar (unbelievers). They don't believe in Allah either.
Therefore, the same question may rise again: If the Kuffar do not believe in Allah, then what sort of evidence will be for them to say "Allah is the witness"? The above verse is, in fact, just a threat by the Prophet (PBUH&HF) to unbelievers, that that will be accounted on the day of judgment for their blasphemy, and he (the Prophet) has enough two witness for that: One is, Allah, the Creator, and the other one is Imam Ali, the Prince of Believers. In general, it refers to all the twelve Imams.
But at that time of the Prophet he was just Imam Ali (AS). Witness to the fact that "he who possesses the Knowledge of the Book" in verse 13:43 refers to Imam Ali (AS) and no other companions of the Prophet, is the numerous traditions reported by both Shia and Sunni.