What account did you configure the task to run as? If it's a local account, then both systems must have a local account with the same name and password. If it's a domain account, then RDP to the source machine with that account and verify that it can access the destination share.
Have you reviewed both the share permissions and the folder permissions on the destination machine?
The task scheduler does not perform a full logon, it does a user impersonation. The main implication is that drive letters are not mapped. Use UNC path notation, \\servername\sharename\foldername.
Add a transcript to your script and capture the error that is occurring.