If they are there, after you remove your account you can delete all the account's email messages from Outlook.com and you'll still have a copy of them at your email provider. If they aren't there, after you remove the connected account, you might want to archive your email messages in a folder in Outlook.com instead of deleting them.

How to Delete Your Gmail Account Without Deleting Your May 19, 2020 How to Clean Out Your Gmail Account and Start Again From The first step is to delete everything in your Gmail account. Now, we can’t be held responsible if you erase a message you later realize you actually needed to hang on to, so proceed at your own

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Learn what deleting your account means: You’ll lose all the data and content in that account, like … How to Delete Gmail Account - Tech Quintal