By the way, you do realize they pulled a fast one in the game series. There was a prequel in there. As such, there was no way the first game occurs in GalCop because Lave isn't colonized until 2412.
The chronological order of the games is actually this (from a lore perspective):
Frontier (prequel to Elite Classic) but actually made as the 2nd game
Elite Classic (this is because Lave isn't colonized until 2412)
First Encounters
Elite Dangerous
The Dark Wheel is run by Jacques and Jacques Station is their base of operations. Jacques though is just a moniker (which means "surplanter"). His old station, Peters Base, in Facece was above Peters Wreck (except that he lived). Jacques is Peter Jameson. The Dark Wheel was not founded by a Ryder. Alex Ryder's father was already a member of The Dark Wheel as was Raffe Zetter so it means it was founded even earlier. I am curious to see if there is a Tesla Roadster onboard Jacques station from Sol. Your beneficiary is Jacques. You received the invite at the beginning. You cannot be invited to what you are already a member.
So, now that we have that out of the way, we know where TDW is based (Colonia). We have a station that was apparently heavily modified if it is capable of thousands of lightyears in a single bound. But here's the catch, there was an attempt to interfere with the jump that was thwarted but it misjumped anyway. Maybe we should have been looking at Colonia and the immediate vicinity all along. Brewer Corporation just built a nice bridge for us, too.
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20 MAY 3302
Freelance Report: Attempt to Sabotage Jaques Station Thwarted
Three individuals carrying pamphlets identifying them as members of 'The Hands of the Architects' have been apprehended at Jaques Station. Starport personnel discovered the individuals attempting to modify the station's frame shift drive.
A station spokesperson said: "The individuals are apparently members of a cult that arose shortly after Jasmina Halsey first claimed to have encountered super-intelligent, non-human life. Materials confiscated from the individuals indicate that they hoped to force a mis-jump during Jaques's forthcoming journey to Beagle Point. Apparently they thought this would give them an opportunity to meet Halsey's 'architects'."
The would-be saboteurs are currently being held in custody at Jaques Station while starport personnel discuss possible extradition with nearby systems.
Note: These events happened in Gliese 1269.