I am in the process of migration Exchange 2010 to 2016 server. Currently I have installed Exchange 2016 which is co-existing with 2010. I have created a test mailbox on the 2016 server. I am able to send e-mails to the test 2016 mailbox from 2010 mailboxes both internal and from public. However I cannot send any e-mails from the 2016 mailboxes to the existing 2010 mailboxes and also to any public e-mail. E-mails from 2016 to 2010 are being stuck in the queue
I don't have the Exchange console in front of me right now, but I had a similar problem, and the counterintuitive workaround for me was to add the specific IP addresses of the new Exchange servers to the Exchange 2010 connector whitelist.
This is despite the fact that its default setting seems to be to allow such traffic for all IP addresses.
Have you received NDRs? What errors show in the NDR? What results show when you run Get-MessageTrackingLog? Run get-queue to check queue type and any queue errors. If you want exchange 2016 to send emails to internet, you should create a new send connector to send emails to internet. Create a Send connector in Exchange Server to send mail to the internet
If you want to send any e-mails from the 2016 mailboxes to the existing 2010 mailboxes, you should create an additional receive connector with specific IP addresses as relays, that include the IP address of the exchange 2016.
More details in the similar case. Internal Email Stuck in Queue During Exchange 2010/2016 coexistence