Mashira uses a brown tube that stretches from the abdomen of his old body to that of his new one that allows him to perform the transfer. He can also transfer part of himself, as he does to the girl. By doing so he can enjoy sex from her point of view as well as his own. He's been body hopping for over 500 years, so this may afford him a level of immortality.
Left Hand refers to him as one of his kind so it may be an ability he shares with Mashira as well. Although Mashira doesn't seem to have the same abilities or even a tenth as powerful as Left Hand, the reason for this is unclear other than like D, Left hand is especially powerful for his race or any other for that matter.