When doing a pre-migration check or copying objects, one of the following message is displayed:

To copy User Alerts, the user will need to have the Manage Alerts permission on the source site AND destination site. The only Default Permission Level that possess the Modify Alert permission is Full Control. If the user is not Full Control on the Site Collections, the Modify Alert permission will have to be added to his permission level. (you can read more on permissions levels and permissions here).

To add this permission, you have to go to the Site Collection Settings -> Site Permissions -> Permission Levels.

Here you can add a new permission level or edit an existing one (if you don't want to edit your existing levels, we recommend to create a new one and give it to the user you are doing the migration with). In the Site Permission section of the Edit screen, you will find Modify Alerts. Check this box to enable Alerts modification for this user on the Site Collection. The user that does the copy must possess the newly modified permission level.