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No, not exactly. She did assume office when Kitz resigned, but then she had to stand for election in 2016. So in fact she was elected to the Governorship, unfortunately.
Per Wikipedia:
Brown ran in the 2016 special election for governor. She faced Julian Bell, Chet Chance, Kevin M. Forsythe, Steve Johnson, and Dave Stauffer in the Democratic primary, and won the nomination.[24][25] By April 2016, she had raised over $800,000 for her campaign in 2016 alone, while her closest Democratic competitor, Julian Bell, had raised $33,000.[26][27]/end_snarkBrown won the election against Republican Bud Pierce, Independent Party nominee Cliff Thomason, Libertarian James Foster, and Constitution Party nominee Aaron Donald Auer, receiving 51% of all cast votes in the state.
Thanks very much, I stand more corrected than not. I’ve only been back once since ‘99 and have largely stopped following the politics—they are a nasty combination of depressing and predictable.