Catalyzes the last two steps in the biosynthesis of 5-methylaminomethyl-2-thiouridine (mnm(5)s(2)U) at the wobble position (U34) in tRNA. Catalyzes the FAD-dependent demodification of cmnm(5)s(2)U34 to nm(5)s(2)U34, followed by the transfer of a methyl group from S-adenosyl-L-methionine to nm(5)s(2)U34, to form mnm(5)s(2)U34. 5-aminomethyl-2-thiouridine(34) in tRNA + S-adenosyl-L-methionine = 5-methylaminomethyl-2-thiouridine(34) in tRNA + H(+) + S-adenosyl-L-homocysteine In the N-terminal section; belongs to the methyltransferase superfamily. tRNA (mnm(5)s(2)U34)-methyltransferase family. In the C-terminal section; belongs to the DAO family.