Catalyzes the covalent attachment of ubiquitin to other proteins. Component of the histone H2B ubiquitin ligase complex (HULC) which plays a role in transcription regulation by catalyzing the monoubiquitination of histone H2B to form H2BK123ub1. H2BK123ub1 gives a specific tag for epigenetic transcriptional activation and is also a prerequisite for H3K4me and H3K79me formation. Also involved in postreplication repair of UV-damaged DNA, in N-end rule-dependent protein degradation and in sporulation (By similarity). Required for obr1 ubiquitination, which regulates mating-type silencing. With cut8, regulates the nuclear accumulation of the proteasome. S-ubiquitinyl-[E1 ubiquitin-activating enzyme]-L-cysteine + [E2 ubiquitin-conjugating enzyme]-L-cysteine = [E1 ubiquitin-activating enzyme]-L-cysteine + S-ubiquitinyl-[E2 ubiquitin-conjugating enzyme]-L-cysteine. Protein modification; protein ubiquitination. Component of the histone H2B ubiquitin ligase complex (HULC) composed of at least brl1, brl2, rhp6 and shf1. Belongs to the ubiquitin-conjugating enzyme family.