Is it possible to use an 8 pin accessory on an iphone 4?
You can read about the differences here

About the adapter You gave in the link, a reviewer wrote:


  If you're looking for an adapter to charge your 30 pin device* with a
  lightning cable, then you will not be disappointed. If you wishing to
  connect your 30 pin device* for sync to your computer*, then you will
  also not be disappointed for at least some 30 pin devices*.


Also many complain that the device they got does not work, so You should look for a more reliable one.

There is a post about this that the adapter stopped working after a new software version: https://discussions.apple.com/thread/5780896?start=15&amp;tstart=0

You should consider buying an USB to 30 pin or a more reliable 8 to 30 pin adapter like this (note that this only allows you to charge the phone. No data transfer)