It seems that you are mixing terminologies here. In Lightroom Classic a catalog is stored on the local computer, keeping track of images stored on the computer hard drive. The term of "migrating" a catalog refers to switching to using Lightroom for the cloud where the images are transferred from the local hard drive to the cloud, and the user no longer uses Lightroom Classic but now uses Lightroom, the new cloud-based version that is currently released at version 4.
If you are using Lightroom Classic, and storing your images on a local hard drive, all that is necessary would be for you to activate Lightroom Classic using your personal Adobe ID and password and open the same catalog because the catalog is not specific to an account. If it is on the same computer, and the images are still organized the same, that is all that would be necessary.
If you are creating collections and sharing those collections in the cloud it would be necessary to reestablish that connection and rebuild those shared collections in the cloud.