If your team can send an email, they can send an SMS
The fastest integration is the one you do not have to build.
Nothing new to install, nothing new to learn
Address an email to the right place and it goes out as a text message. No new software, no training, no project.
It works from systems you cannot change
Plenty of software can send an email and nothing else. That is enough. Monitoring tools, rostering systems and line-of-business applications can all start sending SMS without anyone opening their source code.