Unfortunately, the SFTP protocol doesn't have a "copy" command and it doesn't even support server-to-server transfers, which could be used with FTP to achieve this.
However, SFTP runs over an SSH channel, which means it might be possible to take advantage of SSH remote exec functionality to execute commands at the server. This way, you might be able to execute commands such as "cp sourcepath targetpath" (on Unix-based servers) or "copy soucepath targetpath" (on Windows-based servers) to achieve what you need. Please check out the answer to Remote copy file - SFTP for sample code.