All the image files are saved in this folder:
You can use FTP to download from the source site and upload to the destination site. But this will not automagically link the images to the entries. To do that, you must migrate the data from the source site to the destination.
If you are moving the entire site, then I recommend BackupBuddy or the Duplicator plugin.
If you are moving just the directory, then the process in a bit more complicated because that requires exporting the Connections tables from the WordPress database as a SQl file and then importing that SQL into the new database. Sounds complicated but it actually fairly straightforward. At a very basic level that is all the BackupBuddy or the Duplicator plugin do, except with the entire WordPress database.
Hope that helps!