My question involves alienation of affection law for the State of: Alabama & Mississippi

A couple lives in Alabama and the "other" woman lives in Mississippi where the Alienation of Affection law is legal. The husband leaves the "wife" and moves to MS. The wife of said husband had threatened "writing her book on Alienation of affection against the "other woman" in MS. Since the law is not legal in Alabama, can she travel to the state where the other woman lives and file suit against her?