A Jewish friend insists that, according to his religion, there is simply no afterlife. Is this true and consistent with the Old Testament?

The views of the Jewish people regarding the afterlife vary to some degree. Unlike the Catholic Church, there is no central teaching authority among Jewish people. Thus, in a short answer like this, we cannot fully treat what all Jewish people believe about the particulars of the afterlife. But it is fair to say that most believing Jews do believe in an afterlife. It is also fair to say that the concept of the resurrection of the dead developed in Judaism over the centuries, and became clearer in the later books as God brought the ancient Jews to a deeper understanding of what He was offering. 
 
But for your friend to say that there is nothing in the Old Testament about it requires the dismissal of a good number of texts from the prophets, Psalms and the Wisdom tradition that speak quite vividly of the dead rising (e.g. Is 26:19; Job 19:25ff; Daniel 12:2; Ezekiel 37:12; Hosea 13:14; 1 Sam 2:6, among many others). 
 
At the time of Jesus, the Sadducees did reject the resurrection of the dead, and held that, at death one simply ceased to exist. Part of the reason for this was that they only accepted the first five books of the Bible, and claimed that in them, there was no mention of the dead rising. Jesus sets aside their view by invoking the encounter of God with Moses at the burning bush in the book of Exodus, one of the first five books of the Bible. There, God called Himself the “God of Abraham, Isaac, and Jacob.” But if God is a “God of the living, and not the dead” as the Sadducees would surely insist, then somehow, to God, Abraham Isaac and Jacob are alive. (see Mark 12:24‐27) 
 
And while your Jewish friend is not likely to accept the authority of Jesus, this text goes a long way to show that declaring there's nothing in the Old Testament about resurrection, especially in the first five books, is not an interpretation immune from critique. It further illustrates that at the time of Jesus, while the Sadducees rejected the resurrection of the dead, most other Jews, such as the Pharisees and also followers of Jesus and others, did accept, teach and expect the resurrection of the dead. 
 
Therefore, it seems safe to consign your friend’s remark as the opinion of one Jew, or some Jews, but not all Jews, then or now.