Specifically methylates the pseudouridine at position 1915 (m3Psi1915) in 23S rRNA. pseudouridine(1915) in 23S rRNA + S-adenosyl-L-methionine = H(+) + N(3)-methylpseudouridine(1915) in 23S rRNA + S-adenosyl-L-homocysteine Belongs to the RNA methyltransferase RlmH family.