COPY FILES

The best and perhaps easiest way to do what you are trying to do is use the exact same name (Account User Name) and exact same password for that account on both machines.
You don't have to be logged on to either machine as that particular user but the user must be present on both machines with the appropriate credentials and permissions to the files and folders you are attempting to copy / move.
Don't use blank passwords Windows doesn't like that anymore.
When you are prompted for credentials use the
Machine Name\User Name
and
Password
Format for authentication and tick the box that says remember or save (credentials)
AND
As a last resort (if you really don't care about the consequences then you can also add the "Everyone" group to your permission schema with full control to the folder containing the files and folders you are working with. Make sure to cascade it down to sub-folders and files.

 

As I said above......
You don't actually have to use the accounts they just need to be present and have the appropriate privileges.
And as far as using a blank password to facilitate autologin, you can do the same thing by just by running netplwiz selecting a user (with a password) and BAM.... autologin.
You have to deal with it when you're sharing files across a network as authentication is part of the process, both Share Permissions as well as NTFS Permissions which are configured under the security tab of the file and or folder properties.

 

I used to work for a company that the people in charge didn't care about security, well until it was too late. Their password was password.

Anyway as Trouble suggested just add the "Everyone" group with "Full Control" to the folder.

HERE is tutorial on how to do it.

It is not recommended, but you know that.

Hope this helps.