Depending on if green algae is film or strands determines group. See link below.
Your tank may be mature enough to maintain anemones but it is not biologically mature with competitors & consumers of nuisance algae.
PS. While phosphate may be high, nitratevery low and would be best 5-10ppm
A good guide to identify most of the nuisance algae that plagues the hobby. Complete with pictures and suggested treatments
www.reefcleaners.org
Green Film Algae, Film Algae
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This green powdery film, or cloudiness is caused by a variety of species of microalgae. It is fairly common in tanks of all ages, and tends to be present in some degree at all times. It is only when a bloom occurs that the microalgae becomes so dense as to become noticeable.
Clean Up Crew: Ceriths, Nerites, Astraea spp., most limpets and chitons. Many different species of copepods, amphipods and isopods will feed on film algae as well. Hermit crabs pick at it but are rarely effective against film algae.
Starving it out -Starving it out: Use a phosban reactor, or granulated ferric oxide to remove excess phosphates in the system. Check to make sure you are not feeding any foods that are particularly phosphate rich, or are feeding too much.
Manual Removal: This algae is pretty much the reason they invented the Mag-Float. Time to break it out. A toothbrush will work on the rocks. Change the water, after blasting the rocks with a turkey baster to stir up sediment that may be decaying and adding to nutrients.
Green Hair Algae
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Green Hair Algae or "GHA" is really a broad term that covers hundreds of species of green simple filamentous algae. These species tend to be simple, fine in texture, and have few distinguishable features. True species level identification requires a microscope.
Distinguishing it from look-a-likes: GHA is not coarse or wiry, it should break apart easily when pulled, and should lose form quickly when removed from water. If you can make out a root structure, or a stiff branching structure it is probably not GHA.
Manual Removal: Green hair algae can be pulled out easily, and tooth brushed or scrubbed off the rock work. This is easier to do if the rock is outside of the tank. If it is growing from the sand sift it out with a net.
Clean Up Crew: Assorted Hermits, Blue Legs, Florida Ceriths, Chitons, Turbograzers, Sea Hares, Conchs, Emerald Crabs, Urchins and a few others. It is readily accepted by many herbivores, but because it grows quickly it may persist even in a tank with a fair amount of cleaners.