This story is set right after The Atlantis Complex, to be exact: two weeks before Artemis' 18th birthday. Just on time, some strange group of humans contacts Artemis… with quite shocking news.
The calculations might be off a couple of months, but you get the raw idea, I hope.
the first book was published in 2001, written likely 2000;
Artemis was 12 at this time = birthday of AF was Sept. 1988
AF entered the time stream presumably 2003, came back 2006
end of Atlantis Complex either end 2007 or early 2008
AF is legal 18, infact 15
HM is set to begin in August 2010, thus AF is legal 20, infact 17
For the sake of simplicity, it is assumed that AF needed 2.5 years to overcome Atlantis Complex (the higher you climb, the deeper you fall)
Events of The Last Guardian are ignored here, except for background information about the characters
Birthday of Harry Potter: somewhen 1981
HP and friends likely 29/30 years old at HM set
Battle of Hogwarts 12 years past
12 years is indeed a long time span for the wizarding world to clean up, but that is to be expected after in 1998 pretty much the entire wizarding world lay in smoking ruins. Wizards have the same problem as the People, though to a lesser degree: lots of losses that cannot be offset due to reproduction