Specifically methylates the 50S ribosomal protein L3 on a specific glutamine residue. L-glutaminyl-[ribosomal protein uL3] + S-adenosyl-L-methionine = H(+) + N(5)-methyl-L-glutaminyl-[ribosomal protein uL3] + S-adenosyl-L-homocysteine Belongs to the protein N5-glutamine methyltransferase family. PrmB subfamily. Extended N-terminus.