How does time travel work through superluminal travel, as mentioned in Stephen Hawking's "A brief history of time"?

I quote the part I don't quite understand:

If it is possible for a rocket traveling below the speed of light to get from event A (say, the final of the 100-meter race of the Olympic Games in 2012) to event B (say, the opening of 100,004th meeting of the Congress of Alpha Centauri), then all observers will agree that event A happened before event B according to their times. Suppose, however, that the spaceship would have to travel faster than light to carry the news of the race to the Congress. Then observers moving at different speeds can disagree about whether event A occurred before B or vice versa. According to the time of an observer who is at rest with respect to the earth, it may be that the Congress opened after the race. Thus this observer would think that a spaceship could get from A to B in time if only it could ignore the speed-of-light speed limit. However, to an observer at Alpha Centauri moving away from the earth at nearly the speed of light, it would appear that event B, the opening of the Congress, would occur before event A, the 100-meter race. Thus the moving observer would say that if faster-than-light travel is possible, it should be possible to get from event B, the opening of the Congress, to event A, the 100-meter race. If one went slightly faster, one could even get back before the race and place a bet on it in the sure knowledge that one would win.

I think I misunderstood, but Hawking seems to state in this last sentence that an event can take place (the race) and one can go back in time before it took place (via superluminal travel). That seems ridiculous, since even if one has a teleportation device, which can teleport one over large distances instantaneously, such a feat would not be possible since the event either did not take place or already took place, regardless of whether you're teleporting in or not. Then how would it be possible by going faster than light, which would seem less powerful than a teleportation device?

If I misunderstood, do correct me.

• @J.Schmidt Yeah so the key idea is assumption (b) in my answer. The idea is that you have to create a "triangle" in Minkowski space. This requires using your teleportation machine twice, in two different frames. [I] First you go from event $A$ to spacelike separated event $B$ at time $t=0$ in the unprimed frame. [II] Then you boost by a velocity $v$ such that $A$ occurs after $B$ (it's always possible to find a frame where this happens since $A$ and $B$ are spacelike separated). Then you go from $B$ to an event $C$, which is at the same spatial location as $A$ but an earlier time. (...) Jun 7 '21 at 22:26
• (Note that $A$ is at the same time as $B$ in the original frame, and $C$ is at the same time as $B$ in the boosted frame, and $C$ is always in $A$'s past light cone). Then you just "wait" to go from $C$ to $A$, completing the triangle. Now you have completed a closed time -like loop. You've been able to travel to the past light cone of event $A$ and can cause havoc like killing grandfather's, etc. Jun 7 '21 at 22:28