Hi Val Moore
Thank you for your reply.
If you have made @outlook.com is it the primary alias and your non-Microsoft email is the secondary alias. Then you need to wait at least 48 hours for the alias to take effect. (I apologize for not informing you in time in my last reply)
Secondly you should be sending your email from Outlook Web. I suggest you log into your primary alias @outlook.com in Outlook Web and set the default sender address to your non-Microsoft email address under Settings - Mailboxes - Forwarding and IMAP, Email Aliases.
After waiting for 2-3 days you should be able to send emails, what I want to add to you is that you can send emails using non-Microsoft mailboxes in Outlook Web, but the emails received by the recipients will have the words “Outlook sends on behalf of the recipient” and the recipients who want to reply to the emails from your non-Microsoft mailboxes will need to go to your non-Microsoft mailboxes to view them, you can't view their reply emails in Outlook Web. You will not be able to view their reply emails in Outlook Web.
Thank you for your patience and support!
I wish you all the best
Linda.W-MSFT | Microsoft Community Support Specialist