(a) At any time after dissolution and winding up, a limited liability company may terminate its existence by filing with the Secretary of State articles of termination stating:
(1) The name of the company;
(2) The date of the dissolution; and
(3) That the company's business has been wound up and the legal existence of the company has been terminated.
(b) The existence of a limited liability company is terminated upon the filing of the articles of termination, or upon a later effective date, if specified in the articles of termination.