Reply #3: The Governor cannot "appoint" a successor. .

[annabanana]

Here is the pertinent law:

12-11-1. Special election to fill congressional vacancy--Time of election of representative. If a vacancy occurs in the office of a senator or representative in the United States Congress it shall be the duty of the Governor within ten days of the occurrence, to issue a proclamation setting the date of and calling for a special election for the purpose of filling such vacancy. If either a primary or general election is to be held within six months, an election to fill a vacancy in the office of representative in the United States Congress shall be held in conjunction with that election, otherwise the election shall be held not less than eighty nor more than ninety days after the vacancy occurs.

Source: SL 1890, ch 84, § 19; RPolC 1903, § 1956; SL 1915, ch 182, § 2; RC 1919, §§ 7214, 7308; SL 1929, ch 117, § 5; SDC 1939, §§ 16.0602, 16.1401; SDCL, § 12-11-2; SL 1974, ch 118, § 46; SL 1979, ch 99, § 5.

http://legis.state.sd.us/statutes/DisplayStatute.aspx?Type=Statute&Statute=12-11-1