H.G. Wells' the Invisible Man

Terri Trent, half of the famed singing Trent Sisters, is kidnapped from her London hotel after she witnesses a murder across the street. Toni Trent, her identical twin sister, seeks out The Invisible Man's help in order to rescue her missing sister. Peter has Toni pose as Terri and check back into the hotel, sending the shady manager into a panic.