Hello, @Goran Salamunićcar,
Welcome to the Microsoft Q&A platform!
According to your description, your test email can be found at @yahoo.com and @googlemail.com but not at Microsoft’s email addresses @hotmail.com and @outlook.com.
To solve this issue, the first thing you should do is to check for any non-delivery reports (NDRs) that might provide more information about why the emails were not delivered. These reports can indicate issues like incorrect email addresses, server problems, or policy violations. If you do not receive any NDRs, please use the message trace feature in the Exchange admin center to track the status of the emails. This can help determine if the emails were blocked, delayed, or failed to deliver.
Reference documents:
1.Email non-delivery report (NDR) and SMTP errors in Exchange Online - Exchange | Microsoft Learn
Besides, here are some other steps you can take to troubleshoot this problem:
1.Check the SMTP Server Configuration: Ensure that your SMTP server settings are correctly configured. Sometimes, misconfigurations can lead to delivery issues.
2.Review Email Filtering Settings: Microsoft email services have robust spam and junk email filters. It's possible that your emails are being filtered out before they reach the Junk Email folder. You can review and adjust these settings in the recipient's email account.
3.Check for Blocked Senders: Verify that your sending email address or domain is not on a blocklist. Microsoft email services might block emails from certain addresses or domains if they are flagged as spam.
4.Review SMTP Server Logs: Check the logs on the SMTP server to see if there are any errors or bounces when sending to Hotmail or Outlook addresses.
5.Spam Filtering: Exchange Online has robust spam filtering mechanisms that might block emails from certain senders. Ensure that the sender's email address is not on any block lists and consider adding it to the safe senders list.
Also, a document to help you with email delivery issues is here for your reference: Find and fix email delivery issues as a Microsoft 365 for business admin - Exchange | Microsoft Learn.
Should you need more help on this, you can feel free to post back.
If the answer is helpful, please click on “Accept answer” as it could help other members of the Microsoft Q&A community who have similar questions and are looking for solutions.
Thank you for your support and understanding.
Best Wishes,
Alex Zhang