In the migration method of the invention, for each migration request (MR) recorded in a migration control server (MCS), the following steps are performed in succession: a second mailbox (BOX2) is created in an electronic messaging service system (S2), the first access address (AD1) of the first mailbox (BOX1) that is to migrate from a first messaging service system (S1) is formed as the access electronic address giving access to the users from the outside for the second mailbox (BOX2), and the physical electronic address (ADP1) recorded for the mailbox (BOX1) is changed, in a directory database (DIR), into the physical electronic address (ADP2) of the mailbox (BOX2).