A State High Court has jurisdiction to hear a fundamental right matter even when the Nigerian Army is a party in the suit. According to Section 46(1) of the Nigerian Constitution, a person can apply to a High Court in the state where the infringement occurs for redress. The Federal High Court and State High Courts share concurrent jurisdiction in matters pertaining to enforcement of fundamental rights.

However, it’s essential to note that if the matter falls under Section 251(1) of the Constitution, which outlines the exclusive jurisdiction of the Federal High Court, then the Federal High Court would have jurisdiction. But in general, State High Courts can entertain fundamental rights matters, including those involving the Nigerian Army.