The system enables a user of mobile terminal (T1) to store and access to numerous multimedia files with no limit on size relative to the capacities of his mobile terminal. A sorting centre or a web server (CTM, SW) detects a multimedia file (FM) in a message (MT2) transmitted by a second terminal (T2) in order to extract therefrom an address (AT1) of the mobile terminal, a text block (BT) and a detected multimedia file (FM). A storing space (SSM) stores the extracted multimedia file in corresponding relationship with the extracted address (AT1). The sorting centre or a web server establishes a notification command (CN) including the address (AT1) and the text block (BT). A notification server (SN) transmits a storage notification (NSFM) including the text file (BT) to the terminal (T1).