Catalysis of the reaction: 2,3-bis(3-hydroxytetradecanoyl)-D-glucosaminyl-(1->6)-beta-D-2,3-bis(3-hydroxytetradecanoyl)-beta-D-glucosaminyl 1-phosphate + ATP = ADP + 2 H+ + lipid IV(a).
ATP:2,3,2\',3\'-tetrakis(3-hydroxytetradecanoyl)-D-glucosaminyl-beta-D-1,6-glucosaminyl-beta-phosphate 4\'-O-phosphotransferase activity