Catalyzes the synthesis of Und-PP-GlcNAc-ManNAcA-Fuc4NAc (Lipid III), the third lipid-linked intermediate involved in ECA synthesis. beta-D-ManNAcA-(1->4)-alpha-D-GlcNAc-di-trans,octa-cis-undecaprenyl diphosphate + dTDP-4-acetamido-4,6-dideoxy-alpha-D-galactose = alpha-D-FucNAc4-(1->4)-beta-D-ManNAcA-(1->4)-D-GlcNAc-undecaprenyl diphosphate + dTDP + H(+) Bacterial outer membrane biogenesis; enterobacterial common antigen biosynthesis. Belongs to the glycosyltransferase 56 family.