In the event of a vacancy in the Vice Presidency, the President nominates a replacement, and the Senate confirms the nomination. This process is outlined in Article II, Section 1, Clause 2 of the United States Constitution.
Then I found another explanation:
https://www.usatoday.com/story/news/factcheck/2020/08/20/fact-check-if-vp-becomes-president-house-speaker-doesnt-move-vp/3399838001/
But it's not true that the speaker of the House — or any other predetermined individual — automatically becomes vice president. Upon becoming president, the former vice president would choose another individual to become his or her vice president.
"Whenever there is a vacancy in the office of the Vice President, the President shall nominate a Vice President who shall take office upon confirmation by a majority vote of both Houses of Congress," Section 2 of the amendment explains.
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So I don't know which one is true.
See post 135. And you quoted it again. The 25th Amendment modifies the Constitution, so this is the only Constitutional process to make someone Vice President if there is a vacancy.
Nominated by the president and approved by BOTH houses.