Converts the free carboxyl group of a malonyl-thioester to its methyl ester by transfer of a methyl group from S-adenosyl-L-methionine (SAM). It allows to synthesize pimeloyl-ACP via the fatty acid synthetic pathway (By similarity). The physiological role of BioH is to remove the methyl group introduced by BioC when the pimeloyl moiety is complete. It allows to synthesize pimeloyl-ACP via the fatty acid synthetic pathway through the hydrolysis of the ester bonds of pimeloyl-ACP esters (By similarity). a carboxylic ester + H2O = a carboxylate + an alcohol + H(+) malonyl-[ACP] + S-adenosyl-L-methionine = malonyl-[ACP] methyl ester + S-adenosyl-L-homocysteine Cofactor biosynthesis; biotin biosynthesis. In the N-terminal section; belongs to the AB hydrolase superfamily. Carboxylesterase BioH family. In the C-terminal section; belongs to the methyltransferase superfamily.