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Thanks for the feedback.
First, thanks for Ken’s information.
I understand that you have transferred the mailbox from Office Live Small Business to Office 365. However, the emails cannot be received.
Now, you can try to troubleshoot this issue referring to the following article:
Inbound Mail Flow
If the emails still cannot be received, please help me collect the following information for further research:
1. Check if the emails can be sent from the Office 365 mailbox properly.
2. Check if the issue affects all the users in your company.
3. Provide a detailed non-delivery report (NDR) which is received when trying to send emails to the Office 365 mailbox.
After obtaining the information, I will research it and post the result here on the forum.
Those OLSB business email accounts won't receive any email messages after you moved your domain name.
See / click --> Keep my OLSB
business email accounts?
I would like to confirm that whether the original issue is resolved or not. If not, could you please provide the detailed information required in my previous post?