See Title II, CHURCHES _SUI IURIS_ AND RITES, with Canons 27-41 in the 1990 Code of Canons of the Eastern Churches.
In particular, Canon 31: "No one is to presume to induce in any way the Christian faithful to transfer to another Church _sui iuris_."
And 32, s.1: "No one can validly transfer to another Church _sui iuris_ without the consent of the Apostolic See [ie., Rome].
s.2 In the case of Christian faithful of an eparchy of a certain Church _sui iuris_ who petition to transfer to another Church _sui iuris_ which has its own eparchy in the same territory, this consent of the Apostolic See is presumed, provided that the eparchial bishops of both eparchies consent to the transfer in writing."
Finally, 33: "A wife is free to transfer to the Church of the husband in the celebration of or during the marriage; when the marriage has ended, she can freely return to the original Church _sui iuris_." (Cf. canon 112 in the 1983 Latin Code.)
