The process comprises the steps consisting in: (a) receiving data in a first device, the data containing at least one anticopy protection system identifier; (b) verifying whether the first device is connected to a data recording device by a digital bus; and in case of positive verification: (c) verifying whether the first device comprises a module implementing an anticopy protection system whose identifier is included in the data; and in case of positive verification: (d) offering a user access to the data according to a first mode of access (PPVR) authorizing the recording of the data; and in case of negative verification in step (b) or step (c): (e) offering a user access to the data according to a second mode of access (PPV) not authorizing the recording of the data.