It is due to a DNS internal federation issue. When a mail user sends an email from INSIDE Microsoft Datacenter to you, it is possible that your OLSB mailbox is in the same datacenter. The mail router detects that there is an internal server knowing your email address and the mail does not get out to Internet. This can happen more often than expected, as Microsoft federations include live.com, msn.com, hotmail.com, yahoo, etc.
To overcome this issue, you need to set a rule on your old mailbox to redirect all incoming emails to your Office 365 mailbox. Problem is: you cannot forward to yourself, so you have to use your preliminary identity, ie: alias@mydomain.onmicrosoft.com or something similar. If you destroyed this alias, you need to create any alias with such domain attached to your Office 365 mailbox.















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