Transferring data from one remote system to another under the control of a local system is remote uploading.
Remote uploading is used by some online file hosting services. It is also used when the local computer has a slow connection to the remote systems, but they have a fast connection between them. Without remote uploading functionality, the data would have to first be download to local host and then uploaded to the remote file hosting server, both times over slow connections.
Look up uploading in Wiktionary, the free dictionary.