Catalysis of the reaction: a [methyl-Co(III) methanol-specific corrinoid protein] + coenzyme M = methyl-coenzyme M + a [Co(I) methanol-specific corrinoid protein] + H+.
Catalysis of the overall reaction: methyl-Co(III) methylated-thiol-specific corrinoid protein + coenzyme M = Co(I) methylated--thiol-specific corrinoid protein + methyl-CoM.
Catalysis of the reaction: [methyl-Co(III) methylamine-specific corrinoid protein] + coenzyme M = [Co(I) methylamine-specific corrinoid protein] + H+ + methyl-coenzyme M. This reaction is the transfer of the methyl group from the methylated corrinoid cofactor of a methylamine corrinoid protein to coenzyme M.