A Module, MLR, connected through a cellular communication network to at least a measuring mobile terminal, MMT, at least a mobile switch center, MSC / visitor location register VLR, and at least a machine to machine application, M2MA, characterized in that the module, MLR, comprises a database, BDD, that stores for each measuring mobile terminal, MMT, a universal single identifier, IMSI, a private device identifier, PDID, uniquely allocated to at most one measuring mobile terminal, MMT, said private device identifier, PDID, not being a public subscriber phone number MSISDN and being defined only in the perimeter of the machine to machine application, M2MA, and the address, MSC@, of the mobile switch center MSC / visitor location register, VLR, through which the measuring mobile terminal MMT is connected to the cellular communication network, the module, MLR, being adapted to update a look-up-table stored in the database, BDD, and associating for each measuring mobile terminal, MMT, its universal single identifier, IMSI, and its private device identifier, PDID, and comprising: - at least one short message service center, SMSC, configured to transmit a message sent by the M2MA towards a measuring mobile terminal, MMT, - a home location register, HLR, configured to, in response to a demand from the short message service center, SMSC, regarding said measuring mobile terminal, MMT, request said database, BDD, to provide the short message service center, SMSC, with the address of the mobile switch center, MSC, / visitor location register, VLR, through which said measuring mobile terminal, MMT, is connected to the cellular communication network, in the request from the HLR the MMT being identified by its private device identifier, PDID; - an authentication center, AuC, authenticating said measuring mobile terminal, MMT, the home location register, HLR, the authentication center, AuC, and the short message service center, SMSC, being embedded in a single physical structure forming at least in part the module, MLR, and wherein the private device identifier PDID is formed by the association of an identifier of the subscription and an identifier of the measuring mobile terminal MMT, the subscription identifier identifying or describing the owner and its attachment policy and charging rules, the identifier of the measuring mobile terminal MMT uniquely identifying the measuring mobile terminal MMT in the subscription, the module, MLR, being configured to receive from the database, BDD, said address, MSC@, of the mobile switch center, MSC, / visitor location register, VLR, and the universal single identifier, IMSI, of said measuring mobile terminal, MMT, and is configured, in response, to transmit to said mobile switch center MSC / visitor location register, VLR, using a MAP-MT-Forward-SM communication the message sent by the M2MA based on said address, MSC@, provided by the database, BDD, along with the universal single identifier, IMSI, of said measuring mobile terminal, MMT, provided by the database, BDD. - at least one short message service center, SMSC, configured to transmit a message sent by the M2MA towards a measuring mobile terminal, MMT, - a home location register, HLR, configured to, in response to a demand from the short message service center, SMSC, regarding said measuring mobile terminal, MMT, request said database, BDD, to provide the short message service center, SMSC, with the address of the mobile switch center, MSC, / visitor location register, VLR, through which said measuring mobile terminal, MMT, is connected to the cellular communication network, in the request from the HLR the MMT being identified by its private device identifier, PDID; - an authentication center, AuC, authenticating said measuring mobile terminal, MMT, the home location register, HLR, the authentication center, AuC, and the short message service center, SMSC, being embedded in a single physical structure forming at least in part the module, MLR,