After the file was "successfully" uploaded, I added the following code to the list the contents of the directory (FYI, I Googled it so I don't know if this is the "proper" way to do it).
Originally Posted by Fou-Lu
This prints an empty array, which means the directory itself is empty.
if((ssh2_scp_send($connection, $local_folder.$file_names[$i], $remote_folder.$file_names[$i], 0644)) === TRUE)
echo 'Transfer successful!<br />';
$stream = ssh2_exec($connection, 'ls ' . $remote_folder);
$a = array();
Suspecting that maybe the directory was wrong, I manually put in a test file into the remote directory, but the ls command found it. So I guess that proves that I am at least looking at the same directory that I am trying to transfer to.
I am going to ask my manager if I can get access to another (different) server and see if I can transfer between the two instead of trying to transfer from a server to itself. I'll get back to you when I have some results. Thanks for your help so far, though!
 => test_file.txt