according to conservation of momentum , total sum of momentum of the objects taking part in a collision is same before and after the collision.
Total momentum before collision = Total momentum after the collision
when a cue ball moving at velocity 1.5 m/s hits a billiard ball , transfer of momentum takes place between the balls such that total sum of momentum of cue ball and billiard ball remain same before and after the collision.
hence we say that the momentum is conserved.