Hi @JB105
Unfortunately in normal cases it is not possible to integrate Teams with a third-party mailbox, as Teams stores chat messages, calendar events, free busy status and other data in the corresponding Exchange mailbox.
For more details please refer to this link:
How Exchange and Microsoft Teams interact
For example, if you create a Teams meeting on the Outlook calendar of the mailbox hosted by third-party server, this meeting won't reflect in Teams.
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