A mobile phone of the aforementioned type is known.  The mobile phone includes a streaming server generally compatible with the UPnP (Universal Plug and Play) network protocol, or respectively with the DLNA (Digital Living Network Alliance) interoperability standard, the server then being called a UPnP server or DLNA server, respectively.  Such a server makes it possible to stream media recorded in an internal memory of the phone to a remote client equipment also compatible with the UPnP network protocol, or with the DLNA standard.  The streamed media includes audio and/or video data.  The mobile phone also comprises a web browser including a downloading means for downloading a file from a web server into its internal memory. 
However, the streaming of a file initially stored in a memory of the web server is relatively tedious to implement by the user on a mobile phone, in particular operating under an Android-type operating system.  The user must start by launching the web browser, in order to download the file from the memory of the web server towards its own memory.  This operation in particular requires the user to select the file to be downloaded, and to indicate a location of the internal memory for storing the downloaded file.  The user must then select, using a UPnP or DLNA controller, respectively, the downloaded file to be streamed by the streaming server.