Brown algae can be a bit more challenging to deal with. Yes a UV sterilizer will help, but you'll need to be continually scraping the brown algae off whatever it's clinging to, in order to get it into the water column, where it can then be killed by the UV sterilizer. If you keep doing this you may eventually get rid of it. But if it's stuck on rocks, glass etc. the UV sterilizer won't really help at all.
A pleco will help, if your FH will tolerate it (my Kamfa won't) -- just make sure it's not small enough for your FH to eat; the barbs of the pleco will get stuck in your fish's stomach and he'll die.
But my question is how can a fish destroy his tank with food waste? That's on us, not the fish

Overfeeding, besides causing health issues for your FH, will often lead to brown algae outbreaks.