"Follow us back to Argon Prime" This is a long, slow trip. I don't know if Argon 1 would make it by himself, because there are lots of Xenon destroyers and carriers to take out on the way.
(tip) Help the time pass by using your SETA to cruise around each sector while Argon 1 grinds his way to the next gate.
(tip) It's ok to take time out to dash into Priest's Pity and save your game.  Argon 1 will still be puffing along when you get back.
Once into Argon Prime, make contact again.

Destroy the Xenon Shipyard  (Optional)
This isn't a real "quest"; nobody asks you to do it.  But it's an interesting challenge, and many players seem to do it.  The best time is after you have the 125 MW super shields.