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

Trick question. As we all know the most important interconnect is from the phono stage to the integrated amp.

Actually IF we are ignoring the OP question it’s the microphone cable.

but since we should be trying to help the OP it’s the connection from your CD player to preamp for both information and sonic shaping ( if neutrality is not your goal )

The one closer to the source, except when it isn't. 

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!

Maybe the OP didn't use the correct terminology, but I'll provide an answer to his query. Throw out the part about shaping the sound, it's vague and shouldn't apply. An equalizer and tweaks shape the sound.

IME, the interconnects from CDP to preamp will have the greatest impact and influence on the sound. Start at the source. You want a cable that will faithfully transfer the signal (information) to the preamp.

 

You can easily solve the problem by buying two new cables and inserting one on the CD player and one from amp to preamp.