There is no ethical attorney that can advise you to use a fake SSN on anything. This is one of those things where you are going to have to make a decision as to what kind of risk you are willing to take. While your right to the settlement should not be contingent on you having a valid SSN, any time you use a fake SSN you run the risk of criminal liability and/or deportment.
Good luck to you.
This answer should not be construed to create any attorney-client relationship. Such a relationship can be formed only through the mutual execution of an attorney-client agreement. The answer given is based on the extremely limited facts provided and the proper course of action might change significantly with the introduction of other facts. All who read this answer should not rely on the answer to govern their conduct. Please seek the advice of competent counsel after disclosing all facts to that attorney. This answer is intended for California residents only. The answering party is only licensed to practice in the State of California.
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