It is not possible to transfer Athens accounts between institutions. Users who move between institutions should re-apply on arrival at their new institution for another Athens account.
If a user stays on at the same institution in a different capacity, they will need to contact the Domain administrator who will decide on the course of action. In some cases, it might be easier to give them a new Athens account, as (for example) their group membership or administrator may not be the right one for their new position. They may also be entitled to use more resources.