To execute the transfer of a call between a fixed telephone set of a public telephone exchange network and a cellular telephone of a radio communication network.

These method and device are to transfer a call from a 1st telephone set 10 of a 1st communication PSTN, which includes a call transferring means that is integrated to it to a cellular telephone 12 that is connected to a radio communication network 14. An auxiliary device 16 which works also as a charger to the telephone 12 automatically starts a function that controls start and pause for transfer. The device 16 detects the existence of the telephone 12 on it and initiates a pause or start of transfer.