Amano, first thing you have to know when looking for the connector is the pitch, i.e. the space between pins. It appears that the pitch in this case is 2mm. Measure the distance between pin 10 and 2 (or 9 and 1) on the Atomiswave connector: it should be exactly 8mm.
As for the JST connector, I really doubt you'll find it and even if you do you'll have to crimp the terminals, which means buying an expensive tool: not worth it, I think.
I'd rather suggest you to get this type of connector:
Go to the spanish branch of
www.rs-components.com and type in part number 131-9995 (sorry, direct linking is not possible).
This would be a PCB connector but you can solder wires to its pins easily. Even if it's 20 pins you can cut it in half. The pitch is 2mm and should plug into the Atomiswave. It's a connector normally available at electronics shops, so check there before ordering from that site. The best thing would be to bring the Atomiswave with you to the shop.
As for the female earphone stereo plug, you mean this?
This has 3 pins (left, right, common/ground). Most probably the two stereo speaker negatives on the Atomiswave connector (pin 3 and 7) will both be ground so you can use either, not necessarily both. You solder the 3 wires and you're done...
If you don't know which pin is which on the earphone connector, check with a multimeter.