Low-mass and brown dwarfs have recently been found as wide companions to many nearby stars, formerly believed to be single. Wide binaries are usually found as common proper motion pairs. Sometimes, more than two objects share the same large proper motion, identifying them as nearby systems. We have found a third, low-mass component to a known wide binary at a distance of ~21 pc, consisting of a red and a white dwarf (LHS 4039 and LHS 4040; ~150 au separation) The new companion, APMPM J2354-3316C separated by ~2200 au, was classified as M8.5 dwarf. In recent spectroscopic observations, it shows a very strong Hα emission line and blue continuum. Comparing this event to flares in late-type M dwarfs, we find some similarity with LHS 2397a, a nearby M8 dwarf which is so far the only known example of a low-mass star with a tight brown dwarf companion (separation <4 au). The level of the activity as measured by LHα/Lbol is comparable to that of the M9.5 dwarf 2MASSW J0149+29 both during the flare and in quiescence.