The Exchange web client renders in the Teams website tab now – Chrome and Chromium-based Edge. I use the nightly build of FireFox and it says ‘Blocked by X-Frame-Options Policy’
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This isn’t a way to get new mail notifications in Teams – you’ve got to click over to the tab. But it does let you send a quick message without leaving Teams.
It’s a little inconvenient, though, to have to navigate over to the right channel to find the website tab. You can also create a custom Teams application to access the Exchange website. That’s a little more complicated, but you basically need a manifest.json with static tabs to the inbox and calendar.
Install and open “App Studio” in Teams. Create a new app. Fill in the details — use the generate button to get an app ID. Since you’re not going to publish the app to the Microsoft app store, the info you use isn’t super important … the privacy and terms of use, specifically, aren’t something anyone is going to read.
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And
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In the “Capabilities” section, add a personal tab
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Add a tab for the mailbox:
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If you wish, add a tab for the calendar – I prefer the weekly view, but you can replace “week” with “workweek”, “day”, or “month”.
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In the “Test and Distribute”, click “Download”.
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You’ll get a zip file that you can side-load (i.e. it’s not an app published across the company). In “Apps”, select “Upload a custom app”
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Locate the downloaded ZIP file and open it
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Verify that your app looks right – the permissions are base permissions for all apps (we didn’t add anything special)
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Click “Add” and you’ll be able to select the new app from the ellipses in Teams.
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And you’ll have an app that can access your mailbox
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Or a week view of your calendar
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