How serialize a non-serializable object?

Question

I am using AWS Cognito, and am running into an issue with maintaining a necessary "continuation" object for resetting password between potential app closes. I would like to store the continuation object to sharedPrefs or SQLite using serialization and de-serialization. The continuation object is non-serializable. Is it possible to still serialize it? Here is my attempt

                String serializedObject = "";
                // serialize the object
                try {
                    ByteArrayOutputStream bo = new ByteArrayOutputStream();
                    ObjectOutputStream so = new ObjectOutputStream(bo);
                    so.writeObject(continuation);
                    so.flush();
                    serializedObject = bo.toString();
                } catch (Exception e) {
                    System.out.println(e);
                }
                sharedPref.setPref("Test", serializedObject);


                // deserialize the object
                try {
                    byte b[] = json.getBytes();
                    ByteArrayInputStream bi = new ByteArrayInputStream(b);
                    ObjectInputStream si = new ObjectInputStream(bi);
                    ForgotPasswordContinuation obj = (ForgotPasswordContinuation) si.readObject();
                } catch (Exception e) {
                    System.out.println(e);
                }

I am receiving the following error:

java.io.NotSerializableException: com.amazonaws.mobileconnectors.cognitoidentityprovider.continuations.ForgotPasswordContinuation

Is this even possible to do? Thanks in advance.