will pass on to him/herTransmettrai is the first-person singular future of transmettre. Lui means “to him” or “to her”; the object being passed on may be stated or understood. The other examples include different forms of transmettre, such as the infinitive transmettre and the present tense transmettez.
FR: Je lui transmettrai votre message demain.
EN: I’ll pass on your message to him/her tomorrow.