Identify tiny white connector
As in one of the comments, this does look to be a small pico blade (by Molex) style connector.  It looks a bit odd just because it has the covered flat SMT pins to the sides (gull wings).  These are often used to connect small rechargeable batteries, (eg: As in small in-home wireless phones).  The connector on your "mother board" might be for a small backup battery.   (The male plug part is also in the above link, though you also need to have the crimp pins to insert into the plastic plug piece.  

Here is a similar link for the other connector listing the needed 50058 or 50079 crimp pins:    http://uk.farnell.com/molex/51021-0200/crimp-housing-1-25mm-2way/dp/889477 .  See at the bottom of the page where it shows both connectors, pins already crimped on wires, and even the bare pins).