Catalyzes the ATP-dependent addition of one alpha-linked L-glutamate molecule to coenzyme gamma-F420-2, producing coenzyme alpha-F420-3. Thus, caps the gamma-polyglutamate tail of coenzyme F420 with a terminal alpha-linked glutamate (By similarity). ATP + L-glutamate + oxidized coenzyme F420-2 = ADP + H(+) + oxidized coenzyme alpha-F420-3 + phosphate Binds 2 manganese ions per subunit. Cofactor biosynthesis; coenzyme F420 biosynthesis. Monomer. Belongs to the RimK family. CofF subfamily.