In C# you can't access to other Forms' Controls, but we know that static Members are accessible through other classes. so you should define a static variable in first form to store items in it like this:
In First form decalre the following
public static List<string> myList = new List<string>();
Next in an event of first form add the Listbox(listbox1) items in List
for (int i = 0; i < listBox1.Items.Count; i++)
myList.Add(listBox1.Items[i].ToString());
and in second form you can access this variable by the following and add to listbox2 of second Form
for (int i = 0; i < Form1.myList.Count; i++)
listBox2.Items.Add(Form1.myList[i]);