Easiest? For me? Add them as a collaborator via an email to SMS gateway.
Eg:
https://www.smsglobal.com/services/#emailsms
Easiest for you? Dunno, depends on who your provider is and if they have an API. I guess you should go on their website and find out if they have one mate.
Then figure out what kind of notifications need to be sent and to whom. (Clients, agents, managers, entire teams/departments/organisations) and when (assigned, opened, closed, updated, etc).
These will inform the plugin design.
No point making a plugin without those things.