GO:0004482:   mRNA (guanine-N7-)-methyltransferase activity
Catalysis of the reaction: S-adenosyl-L-methionine + G(5")pppR-RNA = S-adenosyl-L-homocysteine + m7G(5")pppR-RNA. m7G(5")pppR-RNA is mRNA containing an N7-methylguanine cap; R may be guanosine or adenosine.