It's important for the OP to understand that in the absence of a written lease mom (not the OP or her son) has a month to month tenancy with the landlord. Such tenancies can typically be ended with the appropriate written notice (generally a 30 day written notice, although in some states...mine, for example, the landlord must provide 60 days). No reason for terminating such a tenancy need be provided.
If the tenant fails to move after this time period the landlord can then proceed with the eviction process through the court system.
Gail