Connector Identification: Flex Ribbon E-Paper Connector (Kindle 3G)
mezzanine connector

used to connect boards together in a layered fashion

this one is Panasonic AXT434124

mates with AXT334124

https://ca.mouser.com/ProductDetail/Panasonic/AXT334124

found by searching for technical drawings of ED060SC7

here is a breakout board that you could use (you would have to solder the connector)

https://www.amazon.com/Schmartboard-SOP-0-4mm-Pitch-Version/dp/B00OGLBA6C/ref=sr_1_8?ie=UTF8&amp;qid=1514326345&amp;sr=8-8&amp;keywords=SchmartBoard+0.4