Catalyzes the reversible transfer of a formyl group from formylmethanofuran (formyl-MFR) to tetrahydromethanopterin (H(4)MPT) to produce 5-formyl tetrahydromethanopterin (5-formyl-H(4)MPT) and methanofuran (MFR). 5,6,7,8-tetrahydromethanopterin + H(+) + N-formylmethanofuran = methanofuran + N(5)-formyl-5,6,7,8-tetrahydromethanopterin One-carbon metabolism; methanogenesis from CO(2); 5,10-methenyl-5,6,7,8-tetrahydromethanopterin from CO(2): step 2/3. Homotetramer. Belongs to the FTR family. Extended N-terminus.