That is black beard algae. Since you just have fake plants, I'd suggest a bleach solution dip along with a good rinse and a heavy dose of dechlorinator. I will say that I've never done that before so it's just a guess, but I'd think bleach would take care of it. The bad news is that unless you get down to the root cause (the specific imbalance(s) that are causing the problem), it is likely to come back.