You can either declare the list as a variable of the class (outside of your methods) so that it can be used throughout the class, or you an declare it within the A method and pass it to other methods as shown below:
public static void main(String[] args)
{
A();
}
public static void A()
{
ArrayList<String> stral = new ArrayList<String>();
//fill ArrayList
B(stral);
}
public static void B(ArrayList<String> al)
{
//do whatever you want with al
}
Hope this helps!