Does Campaign Monitor support SMS?

SMS is a relatively new feature that is only generally available to some Campaign Monitor customers.  First, I would recommend that you contact Campaign Monitor to check your account.

Our integration supports Campaign Monitor SMS feature. It lets you map a cell / mobile number to Campaign Monitor via our import wizard or field mappings features. In addition, you can map the Consent To Send SMS field from Salesforce to Campaign Monitor again using the import wizard or field mappings.  These fields can only be mapped from Salesforce to Campaign Monitor.

Currently, Campaign Monitor APIs do not support SMS tracking activity, so this information will not flow back to Salesforce. Here is a Campaign Monitor FAQs on SMS which might help - https://help.campaignmonitor.com/sms-campaigns#faq

You can learn more here about SMS settings in regard to our application - https://www.beaufort12.com/campaignmonitor/support/manage-general-settings#SMS-Settings