RadListBox supports item transfer to another (related) RadListBox. By default, the selected item is moved from the source to the destination listbox. You can change that behavior by setting the TransferMode="Copy" property - in this way the item will be copied to the destination listbox.
To enable item transferring you need to:
Set the AllowTransfer="True" property. This will show the move left and move right buttons next to the listbox. You can control the look and feel of the transfer buttons by adjusting the ButtonSettings properties.
Set the TransferToID property to the ID of the destination (second, right) RadListBox. You can use the Smart Tag to add that additional listbox - this will set the TransferToID property automatically.
[Optional] Set the TransferMode property to Copy if you want to copy instead of move the selected item/items from one listbox to the other. By default it is Move.
[Optional] Set the AutoPostBackOnTransfer="True" to fire a postback on transfer.
[Optional] Set the AllowTransferOnDoubleClick="True" to transfer the item when you double click it.
Please check this help topic on how to automatically update the database on transfer.