Gary,
Most likely your AT service does not have permissions to read and/or write the files.
The AT service by default runs with the credentials of the local system account. Scheduled tasks use the same credentials.
To solve your problem, create a domain account and assign permissions both at the source and destination hosts. Then change the scheduler's credentials in control panel; services; select schedule service; startup; and instead of the system account, specify in This Account: the'service' account you just created. Make sure you explicitly mention the domain account as domain\username.