запись

public class Solution {
    public A getOriginalObject(ObjectInputStream objectStream) {
        Object obj;
        try {
            obj=objectStream.readObject();
            objectStream.close();
        } catch (Exception e) {
            e.printStackTrace();
            return null;
        }
        if(obj instanceof A) {
            return(A)obj;
        }
        return null;
    }

    public class A implements Serializable{
    }

    public class B extends A {
        public B() {
            System.out.println("inside B");
        }
    }

    public static void main(String[] args) throws IOException, ClassNotFoundException {
        Solution solution = new Solution();
        A a = solution.new A();

    }
}
вариант 2

public class Solution {
    public A getOriginalObject(ObjectInputStream objectStream) {
        try {
            return (Solution.A)objectStream.readObject();
        } catch (Exception e) {
            e.printStackTrace();
        }
        return null;
    }

    public class A implements Serializable{
    }

    public class B extends A {
        public B() {
            System.out.println("inside B");
        }
    }

    public static void main(String[] args) throws IOException, ClassNotFoundException {
        Solution solution = new Solution();
        A a = solution.new A();

    }
}