Sharing drupal file to a external site We have a site external to our drupal site, but have to use images from drupal site using absolute URL(No way we upload the same images to that site). So we have to provide them with absolute URLs of the images which will be used by the site.

And it should also be possible that we change the images. i.e., If we have to change the image, we have to replace the existing image with the new image with same name.

What is the best way can this be achieved? Anyhow there is going to be a content in our drupal site that contains the image. Will the image URL be the same ALWAYS when I remove the image and upload another image with same name?
Give File (Field) Paths a try:

The File (Field) Paths module extends the default functionality of Drupal's core File module, Image module and many other File upload modules, by adding the ability to use entity based tokens in destination paths and file names.
In simple terms, File (Field) Paths allows you to automatically sort and rename your uploaded files using token based replacement patterns to maintain a nice clean filesystem.