When you click the Select button in a GridView, the SelectedIndexChanged event of the GridView is fired. In this event you can easily access the row which initiated the event and in turn any data you need.
You can find an example at the following page. However, you will need to implement your own logic to add the value from the selected row into the ListBox. Not a very difficult task.
GridView.SelectedIndexChangedGive it a try and see what you come up with. If you get stuck, we are here to help.
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