Can a former employer sue former employee for writing a complaint letter about her direct manager

Without knowing more, it is difficult to formulate a complete answer. Based purely on the facts you presented, it sounds as though she can sue you. But that does not mean that she has a good claim. The standard for filing suit is low. So almost anyone can get sued. The question is whether your former manager's claim has sufficient facts to back her claims up.

Essentially, it sounds as though your former manager may be able to bring a claim for libel, which occurs when a false written statement is published to a third party (whether it be one person or thousand), and is harmed as a result. To have a case, your former manager must prove the statement was false and that she was harmed. You have defenses against these claims. Generally, truth is an absolute defense. Further, you may have had a privilege to send the letter to corporate. Essentially, a privilege means that as an employee, you had a right to convey your observations to more senior management.

States can vary on how these rules are applied, so it is important that you consult an attorney in your state, especially if you have been sued.