Looks legit. Don’t see anything there for blm but number 7 is the muslim brotherhood.
Title tag for the page translates “Unified federal list of organizations , including foreign and international organizations recognized in accordance with the legislation of Russian Federation as terrorist”.
My Google translated your page http://www.fsb.ru/fsb/npd/terror.htm from Russian.
It lists 24 terrorist groups to 8-12-2015. I didn’t see BLM on the list.
Maybe I missed something. I would like to think this is legit, but I am suspicious.