Simple paradox example

I'll try to keep this simple (mainly for my own benefit; being a dopey engineer and not a physicist, it took me a while to clearly see the causality violation in FTL). I apologize for any inaccuracies this may have.

Say the lost Orion party craft flies past the earth at 0.866c, headed toward Proxima Centari (which, since I don't have my references handy, I'll fudge and say is 4 lightyears away). As they zoom past, they send us the schematics for an ansible, some sort of FTL communications device.

Now, in our reference frame they will arrive at PC in 4.62 years. Say it only takes the brilliant earth scientists a year to decode their language and build the ansible, but the UN can't decide what to say to them until they reach PC. When send them a congratulatory message as they zoom past PCentari, only 2.31 years would have passed for them, in both reference frames, but this is enough time for them to get to PC in their RF due to length contraction.

Now, since they see us as moving past them at 0.866c, in their reference frame they see us as experiencing time dialtion as well, and in that RF only 1.15 years has passed on Earth. Now, according to SR, their reference frame is just as valid as our own. So, when they use their ansible to send a message back, it is received on Earth, in both reference frames, 1.15 years after they left the Solar system, which is 3.47 years before we sent them the message. Causality is violated.

Now note that nowhere in this discussion is the nature of the FTL communication stated. The ansible could be a hyperspace wave radio, a warp drive message torpedo, a instantaneous matter transmitter, or any other device. The only assumptions required are that Special Relativity (which has been rigorously tested) is accurate, and that the FTL communication device can cross from one reference frame to another. If you disallow the latter, then FTL and causality may both be retained, according to my limited understanding. This is the case for both the "Alderson Jump Drive" of Motein God's Eye and the FTL teleport in The Nimrod Hunt. In the former, a reference frame is defined by the two corresponding Alderson Points, and the ship "jumps" point to point in that RF. In the other, a universal RF is defined by the builders of the teleport stations.