S-adenosyl-L-methionine-dependent methyltransferase that mediates mRNA cap2 2'-O-ribose methylation to the 5'-cap structure of mRNAs. Methylates the ribose of the second nucleotide of a m(7)GpppG-capped mRNA and small nuclear RNA (snRNA) (cap0) to produce m(7)GpppRmpNm (cap2). Recognizes a guanosine cap on RNA independently of its N(7) methylation status. Display cap2 methylation on both cap0 and cap1. Displays a preference for cap1 RNAs. a 5'-end (N(7)-methyl 5'-triphosphoguanosine)-(2'-O-methyl-ribonucleoside)-(ribonucleotide) in mRNA + S-adenosyl-L-methionine = a 5'-end (N(7)-methyl 5'-triphosphoguanosine)-(2'-O-methyl-ribonucleoside)-(2'-O-methyl-ribonucleotide) in mRNA + H(+) + S-adenosyl-L-homocysteine