(6S)-5,6,7,8-tetrahydrofolate + ATP + formate = (6S)-10-formyltetrahydrofolate + ADP + phosphate One-carbon metabolism; tetrahydrofolate interconversion. Mutant cannot degrade vanillate or syringate, but it can degrade protocatechuate and 3-O-methylgallate (PubMed:9501423). Mutant shows O-demethylation activity toward both vanillate and syringate in the presence of tetrahydrofolate, indicating that ligH is not directly involved in the O demethylation of vanillate and syringate (PubMed:15090517). Belongs to the formate--tetrahydrofolate ligase family.