A fascinating question, I'd love to see it in action. The truth is I don't know for sure but I felt compelled to answer as I posed a very similar question around 4 years ago on several forums without reply.

I phrased it as pushing a fixed rod of a similar length to activate a switch on a light bulb; hence allowing a morse code message to be sent measurably faster than light as the lateral movement would transmit instantaneously.

However, this cannot be as the FTL (faster then light) transmission should not be possible. Therefore, the only answe can be somehting liek this:

If we reduce the string that you use in your thought experiment to its constituent parts then it is a compound material that, at a molecular level would be polymers or monomers, that are bound by the electroweak force as the atoms bind covalently (electron shells) to form the stable compounds that make up the string. As each tiny part of the string is exerting the pulling force via this binding then the force will ultimately be reduce to the transferral of this force at this atomic level. Hence the force carrying particles or bosons would be limited as 'travelling' at no more than the speed of light. So, the force would be a light speed (or less) ripple along the length of the string. So your partner at the end of the string would not feel the force any faster than the speed of light so causality is not violated.

I'd be fascinated if this was wrong though.