The governor of any state cannot appoint a member to the House of Representatives when a vacancy occurs before the expiration of a term. All a governor can do is call a special election; the Constitution is clear about that. Article I, Section 2, Clause 4:
When vacancies happen in the Representation from any state, the executive authority thereof shall issue writs of election to fill such vacancies.
The governor of any state cannot appoint a member to the House of Representatives when a vacancy occurs before the expiration of a term. All a governor can do is call a special election; the Constitution is clear about that. Article I, Section 2, Clause 4:
When vacancies happen in the Representation from any state, the executive authority thereof shall issue writs of election to fill such vacancies.