Do Teams free and Teams for your personal life work together?
Teams with a personal account is for use in your personal life. Teams free is a free experience of the enterprise version of Teams that can be used for your business. There are limitations to Teams free vs. Teams for business use. Learn more about finding the right Microsoft Teams for you.
In the current state, there is no interoperability between Teams for your personal life, Teams free, and Teams for work. You cannot message work accounts or accounts using Teams free from the Teams for personal life experience.