It comprises a Short Message Service Center (2) (SMSC), STP nodes (4) (Signal Transfer Point), Home Location Register (3) (HLR) and Visitor Location Register (VLR); it is characterized in that it comprises additional SMS storage means (5) and storage means (3 or 4) of an identification of said additional SMS storage means (5), which relates the identification of the means (5) with their address in the mobile network, so that when sending a number corresponding to the identification of the means (5), means (3 or 4) are consulted, from which means the address of the network associated with the identification used as a VLR address for sending the SMS to means (5) is obtained, being stored in these means as if they were a mobile terminal. Storage is carried out such that each mobile terminal subscriber uses the identification of the means (5) for sending an SMS, which had previously been received or generated, in the same manner as it does when it sends an SMS to another mobile terminal.