Yes, you can sue your former client if they are using your personal information, such as your name and social security number, without your permission to fraudulently enter into financial transactions. This conduct violates too many laws to list.
The question is what damage has this caused you and what type of relief you wish to seek. You should probably seek some form of injunctive relief to immediately stop this person from using your personal information. If you have sufferred some type of economic harm, which would include damage to your personal credt rating, then you should attempt to sue for monetary damages. Finally, you can make a criminal complaint to your local law enforcement authorities, who may wish to prosecute this as a crime.
You should consult with a lawyer who has experience in identity theft cases to explore your options and protect youself from further harm.
Legal Information is Not Legal Advice
My answer provides information about the law based on the limited information provided in the questions asked and is not intended to provide legal advice or opinions, and does not constitute an attorney-client relationship. The answer to the question is for educational and informational purposes only. The law differs in each jurisdiction and may be interpreted or applied differently depending on the jurisdiction or situation. Accordingly, I highly recommend that you consult with an attorney to discuss the details of your problem so you can get legal advice tailored to your particular circumstances.
Yes. You should immediately talk to a local attorney. The longer you wait, the bigger the mess they can be creating for you. Call your local attorney Bar Association and ask for a referral to an attorney who handles identity theft cases, right away.