Which is more important in transmitting the sound, the information...

Ha! No! Not even close!

IF we actually answer the OP then it doesn’t matter. Both are equally important. ALL are equally important. For both A and B, which are repetitive anyway since "shaping the sound" (whatever that means) is included in "max information transfer." So the question itself is garbled. But IF we are gonna take it seriously then the question that should have been asked is which one will give me the most improvement. And the answer to that one is: replace whichever one is worse.

Unless by "shaping the sound" he means messing around with it. In that case replace either one, won’t matter, unless one of them is already messing around more the way you like it messed up than the other, in which case keep that one.

How to tell? As always, we don’t know! We can’t tell! You can only listen and decide for yourself! Which is why its a trick question! (Although not really- you have to listen and decide for yourself is ALWAYS the correct answer!)

Thanks guys - I now realize what a foolish question it was...

It is not that the question is foolish, but it does demonstrate ignorance. The answer is more complicated than anyone who has responded in the thread (aside from myself) understands. 

For A) for max information transfer?

For B) for shaping sound?

This is too ambiguous.  What do you mean by "information transfer"?
And what do you mean by "shaping sound"?  I don't even know what those mean.  

As for "max information transfer", the information transferred is the same, so there is no "max".  I think you meant "max fidelity transferred".

As for "shaping sound", you probably meant "filtering affect" since every cable is a "filter" - for example a cable making the sound warm, neutral, upfront and so on.

Not sure why this question is causing so much confusion. The OP is asking whether he/she should first upgrade the CD to pre-amp or the pre-amp to amp IC.

And I'll avoid the short answer (which is that interconnects don't make much difference) because there's a LONG meandering thread on that already.

MC - great answer!