How to grant permissions to Network Service to write in a remote location
Solution 1:
Grant rights to the remote resources to the computer account; this will allow for NETWORK SERVICE to access the resources.
Note that for this to work, the systems must be in a domain.
When granting permissions, Computer accounts aren't searched by default. You'll need to change your search scope in the permission granting dialog:
Then select the computer that the NETWORK SERVICE is running as.