Why did Allaah address the Jews during the reign of the Prophet, sallallaahu 'alayhi wa sallam, with the sins that their ancestors did at the time of Moosaa (Moses), may Allaah exalt his mention, like the killing of Prophets and their transgression in the Sabbath? Please clarify when the successors will be held accountable for what their predecessors did?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah and that Muhammad is His Slave and Messenger as well as that of his family and all his companions.

Allaah Says (what means): {…and no bearer of burdens will bear the burden of another.}[Quran 6:164]. This means that a soul is not sinful for the sins that others have committed. Every soul is only held accountable for the sins that it itself had committed, and it will be punished for its own sins only. This is the rule which is confirmed in the verse in regard to all people, whether Muslims or non-Muslims, Jews or Christians. On one hand, the Jews at the time of the Prophet were not held accountable for the sins of their fathers. However, they acted in the same manner as their forefathers did in rejecting the truth which the Prophet brought to them and altering the books that were at their hands, and this is what exactly their forefathers did with the Prophets, may Allaah exalt their mention, who were sent to them. It is for this reason that the news about their forefathers came in the form of an address to the present ones. Allaah Says (what means): {But it is [not] that every time a messenger came to you, [O Children of Israel], with what your souls did not desire, you were arrogant?}[Quran 2:87]. Allaah further Says (what means): {And Moses had certainly brought you clear proofs.}[Quran 2:92]. On the other hand, the Jews of the time of the Prophet matched their forefathers in their crimes and they did not disown and disassociate themselves from the heinous crimes of their forefathers. Hence, the message came as an address to them. 

Allaah Knows best.