Your best course is to cooperate fully in the investigation and to make sure that your employer knows that you have a difficult and irresponsible former spouse who may be behind this.
In Georgia, most employment is considered "at will" which means that either the employer or the employee may terminate the relationship at any time, for any reason. There are exceptions such as where there is an employment contract, where the employee is represented by a union with a collective bargaining agreement in place, or where the employer's action is based on illegal discrimination, that is, a prohibited basis such as race, gender, religion, etc. There are a few other exceptions as well: an employer is also prohibited from terminating at-will employees as a method of retaliation if the worker has sought an investigation into prohibited discrimination or has filed a legal claim for discrimination against the employer. Furthermore, employers are prohibited from firing employees who take leave for family or medical purposes pursuant to FMLA. Lastly, employers cannot fire employees who are simply exercising a legal right, performing an obligation under law, or refusing to do an illegal act.
Your post does not raise any facts suggesting that any of the exceptions to the at will doctrine might apply to your situation.
In an at will state, the employer is not under a legal duty to state a reason for termination and, if a reason is given, it does not have to be the true reason. In fact, in an at will state,the employer does not have to investigate and determine the truth of any concerns or doubts about the employee. However, in your case it seems that your management is handling the situation with due regard for fairness and allowing you to offer your position in the matter.
My responses to questions on Avvo are never intended as legal advice and must not be relied upon as legal advice. I give legal advice only in the course of an attorney-client relationship. Exchange of information through Avvo's Questions forum does not establish an attorney-client relationship with me. That relationship is established only by individual consultation and execution of a written agreement for legal services.
I agree with the previous response that you should allow HR to conduct an investigation into the situation. You may want to share with them that you have an ex-husband that is vindictive and likely to do something like this.
Any response to general questions is intended for general purposes only and is not intended to be legal advice. Further, responding to a general question does not estalish an attorney-client relationship.