Original Article: https://social.technet.microsoft.com/Forums/Azure/en-US/65f67962-582a-4af1-854d-8fd5e8888a04/how-to-send-a-file-to-other-computers-via-group-policy?forum=winserverGP


File preference items allow you to copy, modify the attributes of, replace, and delete files. (To configure folders rather than individual files, see Folders Extension.) Before you create a File preference item, you should review the behavior of each type of action possible with this extension.

To create a new File preference item

  1. Open the Group Policy Management Console. Right-click the Group Policy object (GPO) that should contain the new preference item, and then click Edit.
  2. In the console tree under Computer Configuration or User Configuration, expand the Preferences folder, and then expand the Windows Settings folder.
  3. Right-click the Files node, point to New, and select File.
  4. In the New File Properties dialog box, select an Action for Group Policy to perform. (For more information, see "Actions" in this topic.)
  5. Enter file settings for Group Policy to configure or remove. (For more information, see "File settings" in this topic.)
  6. Click the Common tab, configure any options, and then type your comments in the Description box. (For more information, see Configure Common Options.)
  7. Click OK. The new preference item appears in the details pane.

Also you can use startup or logon script to copy files, refer to
copy a file from share to local filesystem
http://social.technet.microsoft.com/Forums/en/winserverGP/thread/c607b501-0cb0-4eb8-830a-641de76488bc

For more information please refer to following MS articles:

Configure a File Item
http://technet.microsoft.com/en-us/library/cc772536.aspx
Group Policy Preferences Getting Started Guide
http://technet.microsoft.com/en-us/library/cc731892(v=WS.10).aspx