Why might outbound email not work after an Exchange 2016 hybrid migration to Exchange Online?

Question

Microsoft Exchange

Hello! I'm trying to transfer the mail of employees in my organization.
Published local Exchange 2016 on the web, connected MRSProxy on it. Then, through the EAC, I enabled the hybrid migration mode, logged in to office365, and also enabled hybrid migration. I downloaded the Windows software in the process, she set everything up for me. Further, in Exchange Online, I created a remote mailbox migration package and migrated 1 mailbox in this way. Now what I have:
The test box is in the cloud, in the local exchange it is written that this is an Office365 user. Through outlook online I go to mail without problems. Incoming mail works at the old address, but outgoing mail is not sent to any. I can only send to myself, then everything will come, it also works for external addresses such as mail.ru, etc., but for the addresses of other employees who are in the local server - letters do not come from this mailbox.
What have I done wrong? I need to transfer all the boxes, after which I can change the MX records to office365, but what should I do before replacing the records? It seems that hybrid migration is just what is needed in order to move long and dreary? And then it turns out that if my box moved online, then only incoming mail works on it

Answer 1

In general, the problem was in the connector to the local server from the cloud. We have several domains and the error was with this one. Thanks to all!

Answer 2

but outgoing mail is not sent to any

it also works for external addresses like mail.ru, etc.

well, well
, on the topic - check MX records and logs

Answer 3

https://docs.microsoft.com/en-us/exchange/hybrid-d...
https://docs.microsoft.com/en-us/powershell/module...
https://docs.microsoft. com/en-us/powershell/module...

-Features
Centralized: Enables transport servers to handle all message transport between the on-premises Exchange and Exchange Online organizations, including external message delivery to the Internet for both organizations. If this value is $false, the on-premises transport servers and Exchange Online organization are each responsible for their own Internet message delivery.

well,
https://docs.microsoft.com/ru-ru/exchange/transpor...