FFC 13 pin cable extension
I think in your situation the easiest way would simply be to use a 13 contacts to 13 contacts board, then a new 13 pin FFC cable. 




Both can be bought from common suppliers. These two are specifically from amazon. 

13 pin adapter board

13 pin FFC 150mm cable

While I'm pretty sure your pitch is 1.0mm....measure it yourself to be sure.