What if an illegal immigrant obtains US identity, then marries in US, and buys property, what happens to everything after they die?

What if Jane Doe lived in Bombay, India with her son (John who was in the US then deported for drugs) and then comes to the US, by way of Cuba (right before the US closed it''s borders to Cuba). She took up a false name (Mary Todd) to come to the US. Then obtains legal documents under her new assumed name Mary Todd, gets married, buys property and lives under that name. She then brings her only real sister, Sue Smith, to the US. Sue Smith comes to the US under her correct legal name and establishes legal roots in the US as a legal citizen. Mary Todd (Jane Doe) dies but has all her assets and property under Mary Todd, who can inherit her estate? John her son in Bombay who was deported? or Sue Smith her established sister in the US? or both. What advice would you give Sue Smith? Because she is the only one that can claim the body what should she put on Mary Todd''s (Jane Does) death certificate?