Even if you are not running Linux, this is of some value:
http://tiagovaz.wordpress.com/2008/01/04/using-a-hl-340-usb-serial-adapter-against-2623-linux-kernel/
Using a HL-340 USB Serial Adapter against 2.6.23 linux kernel
This device is:
idVendor 0x4348
idProduct 0x5523
Those 2 numbers are the USB device's unique ID that links it to the driver.
You'll need to search for a driver for those IDs for your operating system.