Sending, receiving, and organizing email in Outlook.com
Try changing your primary alias in your Microsoft account settings. Since you already added the @outlook.com address, setting it as primary should automatically make it the default sender address.
- Sign in to your Microsoft account at account.microsoft.com.
- Go to the Your info tab at the top.
- Select Edit account info or Sign-in preferences.
- Under the "Account aliases" section, locate your @outlook.com address.
- Click Make primary next to the @outlook.com address.
Note that it may take up to 48 hours for this change to fully sync across all Microsoft services, including Outlook.live.com browser settings. Alternatively (if the above doesn't stick) in Outlook.live.com, go to Settings (gear icon) > Mail > Sync email. Under "Set default 'From' address," you should be able to choose the desired address directly.
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hth
Marcin