We will demonstrate how to copy value from one ListBox to another ListBox without deleting the values from the list box. Lets create two listboxes: lstAvailableItems and lstSelectedItems AND two buttons: btnAdd and btnRemove.
Below is the code to add items from lstAvailableItems to lstSelectedItems after clicking the Add button. We can remove the items from lstSelectedItems by clicking Remove button.
Below is the design of the form used for this example.

private void btnAdd_Click(object sender, EventArgs e)
{
string lstboxItem = lstAvailableItems.GetItemText(lstAvailableItems.SelectedItem);
lstSelectedItems.Items.Add(lstboxItem);
lstAvailableItems.GetItemText(lstAvailableItems.SelectedItem);
}
private void btnRemove_Click(object sender, EventArgs e)
{
lstSelectedItems.Items.Remove(lstSelectedItems.GetItemText(lstSelectedItems.SelectedItem));
}