In the end, Rose failed to say anything. She wanted to turn down the offer. She wanted to cut ties with him, to say that they can't meet again, but she couldn't bring herself to do it.
Whether it was the influence of Monica's words or her own desire to escape, Rose couldn't stop herself from clinging to that small hope—the hope that she would be able to escape. The hope that she could start a new life with the man she had grown to adore.
Sirius took a few photos he needed to create a new identity for her. Apparently, he was doing the same for himself as well, registering them as siblings to make it possible for the two of them to travel without problems.
