Catalysis of the reaction: N-acetyl-D-glucosaminyldiphosphoundecaprenol + UDP-N-acetyl-D-mannosamine = N-acetyl-beta-D-mannosaminyl-1,4-N-acetyl-D-glucosaminyldiphosphoundecaprenol + UDP.
UDP-N-acetyl-D-mannosamine:N-acetyl-beta-D-glucosaminyldiphosphoundecaprenol beta-1,4-N-acetylmannosaminyltransferase activity