Electronic – Identify molex connector

The cable is a "flat flex cable" (FFC). The connector is one of several hundred different types made for FFCs. Without a LOT more information it would be almost impossible to narrow it down further.

For starters, we don't know the manufacturer. Look carefully at the connector and there might be some identifying marks. Next would be to know what the conductor pitch of the cable is. Common values are 1.0, 0.8, 0.65, and 0.5 mm. Those two pieces of info, along with what you've already given us, might narrow it down to at least a product series.

Without precise measurements it's a little hard to tell, but I am pretty sure that its a JST XH series connector. A datasheet for these connectors can be found here.

The OP has since tested and confirmed this to be the correct part.