The typesetter for the 1852 LDS edition accidentally misread this church as his church. For the second printing of that edition, the error was caught and corrected (probably by reference to the 1840 edition). Of course, his church would work since the antecedent for the his would be the preceding God (in “after the holy order of God”).
Summary: Maintain in Alma 5:54 the original reading this church in “they have been brought into this church”.