Select the folder where the backup will be written. This can be a subfolder of the share.
Right-click and select Properties.
Select the Security tab.
Click the Permissions button.
Set the MS SQL services user account (the one that MSSQLServer and SQLServerAgent are using for logon on the source machine) to be listed with Change access. The account needs the ability to read from that folder, write to that folder and create new files and folders in that folder.
Click OK until all dialogs are closed.
For more information on permissions, security, and access type, refer to the Windows Help system.