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This isn't enough. You need to very clearly state that her conduct while on the job is THEIR business, and THEY are responsible if she is slandering. You need to specifically tell them what you want: for them to intervene to prevent this from happening ever again, that you will hold THEM accountable if it does. Don't talk around the topic. Tell them exactly what happened, although you do not need to go into the detail of the lies.
Something along the lines of:
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Dear Ms Regional Director:
As you recall, I worked for _______________ Department from ___________ to _____________. Several days ago a former client sent me a rather disturbing message. She went to lengths to find a way to contact me as we have not been in touch since I left ___(department).
Her new ____________ (whatever mil's position is) was visiting her for the first time. In the course of small talk conversation to establish a relationship, my name came up as the client's previous ___ counselor. ____________(mil's name) began to spew forth all manner of lies and slanderous statements about me. This is unacceptable and unprofessional. I want _____________(mil) held accountable for her actions, and I want this to never happen again. Please let me know what corrective measures you have undertaken.
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It's up to you as to whether you inform them of your relationship with mil or not.