How to have a common method to perform same action with two different instances of user objects?

Here is how the code I am working on is currently looking like:

Class A {
   boolean someVariable;
   String  anotherVariable;
   //getters and setters
}

Class B {
   boolean someVariable;
   String  anotherVariable;
   //getters and setters
}

Class LetsSayMainClass {
   //init instances for A and B class
   performThis(a);
   performThis(b);

private boolean performThis(Object obj) {
     if (obj instanceof A)
        //assign a variable with the value of obj type casting to A
     else if (obj instanceof B)
        //assign a variable with the value of obj type casting to B

     if (obj.getSomeVariable)
       //Do Something
     if (obj.anotherVariable.isEmpty())
       //Do Something

   }
}

The Classes A and B have common variables and methods over which I would like to perform some checks. I cannot alter these classes to have a common implementable interface and factory to instantiate better. So, at this point, as the checks to be done are common for both of these classes, I am trying to use a single instance in the performThis method to avoid code repetition.

I cannot do something like this in the performThis method

private boolean performThis(Object obj) {
     if (obj instanceof A)
        obj = (A) obj;
     else if (obj instanceof B)
        obj = (B) obj;
     if (obj.getSomeVariable)
       //Do Something
     if (obj.anotherVariable.isEmpty())
       //Do Something

   }

The if conditions using the variables would throw error as they would still see the obj as an instance of Object than of either A or B.

I could have two different methods to take care of this issue. But, ts there a way to avoid the code repetition? Something I could use with the existing setup?

I probably wouldn't do this but, if you insist on having no repetition, one thing you can do is join the types as a proxy.

class AorB {
  A a;
  B b;

  public AorB(Object o) {
    if (o instanceof A) {
      a = (A) o;
    } else if (o instanceof B) {
      b = (B) o;
    } else {
      // throw something?
    }
  }

  public boolean getSomeVariable() {
    return isA()
      ? a.someVariable
      : b.someVariable;
  }

  public String getAnotherVariable() {
    return isA()
      ? a.anotherVariable
      : b.anotherVariable;
  }

  public boolean isA() {
    return b == null;
  }

  // rest
} 

That would allow you to define performThis like so:

 private boolean performThis(Object obj) {
     AorB aOrB = new AorB(obj);      
     if (aOrB.getSomeVariable())
       System.out.println(aOrB.getAnotherVariable());
     if (!aOrB.getAnotherVariable().isEmpty())
       System.out.println(aOrB.getAnotherVariable());
     return aOrB.isA();
 }  

And use it like so:

class Main {
  public static void main(String[] args) {
    A a = new A();
    a.someVariable = true;
    a.anotherVariable = "This is an A";
    B b = new B();
    b.someVariable = true;
    b.anotherVariable = "This is a B";
    LetsSayMainClass lsmc = new LetsSayMainClass();
    lsmc.performThis(a); // prints "This is an A" 2x
    lsmc.performThis(b); // prints "This is a B" 2x
  }
}