The story was either in Analog or Asimov's probably. There's a slight chance it could have been Magazine of Science Fiction & Fantasy but I don't think so.
Father invents a teleportation device in the nick of time to send his son away before soulless absorptive Borg/Berserker-like alien machines descend and take over in their relentless march across the galaxy. There may have been a pod-people like aspect to the takeover, so more Borg (personality-subsuming/destroying) than Berserker (eg, total physical destruction).
Son survives to fight for humanity's survival or maybe he's the last human? I think he works on trying to recapitulate the technology of the transport mechanism? Something like that, but that's not the important part.
I can't put my finger on it, might have just been where I was in my life at the time, but I found the passages around the father urgency and despair sending the son away particularly, hauntingly affective and would love to read it again.
The dates 1999-2007 are extremes, I think it was closer to the center of that time span, probably 2003-2005.
I tried looking through back issues that I had on hand, a couple of years later, but no luck. "Transporter" or anything like it is such a common thing that I have had no luck with search engines.