The Watchtower Society said that people baptized in another religion, have to be baptized as one of Jehovah's witnesses. Up until 1918, Bible Students rebaptism was not necessaryl ( Only those baptized before 1918 did not have to be baptized again. While the exact details of Charles Taze Russell's personal baptismal practices before 1918 are not definitively documented, the organization later established that immersion before 1918, coupled with a shift away from a previous religious affiliation and affiliation with the Watch Tower, was considered valid.)
(1931 the Watchtower Society changed it to Jehovah's witnesses though there continued to be Bible Student groups after that, but not associated with Jehovah's witnesses). Yes, the Watchtower Society says you must be baptized through the WTS procedure for baptism to be considered officially one of Jehovah's witnesses. A record is kept of that in the congregation files, and notification if you move is sent to your new congregation. But in 1956, is was stated definitely, people needed to be rebaptized by jws.
WT 1956 July 1 p. 406 pp.14 “Often the question is asked whether one baptized previously in a ceremony performed by some other religious group should again be baptized when coming to an accurate knowledge of the truth and making a dedication to Jehovah. Because of what has been already said, now there is compelling reason for also saying, Yes, one must be baptized again. Obviously, by any of such religious systems one was never in reality baptized “in the name of the Father and of the Son and of the holy spirit,” because had he been so baptized he would have appreciated the authority and office of such true Higher Powers. And if previously dedicated to Jehovah, the individual would have separated himself from such God-dishonoring Babylonish systems even before letting them baptize him. So the act of being baptized is not the important thing, but, rather, that which the act symbolizes is the element of importance.” January 15, 1989 Watchtower p. 13 "To become one of Jehovah’s Witnesses, then, a person must be a believer—one who exercises faith and gets baptized. Even before baptism, such faith manifests itself in godly conduct, trust in Jehovah, participation in the Kingdom-preaching work, and acceptance of Jesus’ ransom sacrifice. Faith in the ransom is emphasized for baptismal candidates, for the first of two questions the speaker asks them is: “On the basis of the sacrifice of Jesus Christ, have you repented of your sins and dedicated yourself to Jehovah to do his will?” Only if the individual answers in the affirmative and also understands that his dedication and baptism identify him as one of Jehovah’s Witnesses in association with God’s spirit-directed organization can he acceptably undergo water immersion. (The WTS does recommend sending a letter to the non-jw religion you were associated with, especially currently or in the near past.)
