The invention concerns a method and a device for communicating between at least a first terminal (15) and a second terminal (12), a first communication session (S1) having previously been established by the first terminal, and first drawing data intended to be transmitted to the second terminal having been generated (E206) by at least the first terminal. When the second terminal is not available to participate in the first communication session, the communication method stores (E209) said first drawing data in a communication device. After the end of said first communication session, the communication device sends (E215) an invitation message to the second terminal inviting it to participate in a second communication session (S2) and transmits (E219) said first drawing data to the second terminal during the second communication session.