I have configured Exchange 2016 and Zimbra with same domain name.
I am able to send mail to email user of zimbra server.
In Zimbra , configured a transport file which routes the mentioned email addresses to relay to exchange server.
But mail is bouncing back from exchange server.
Also, if there are any differences between your initiated send to Zimbra + Exchange.
So, for both sends, are you using the same client? relay settings? host/IP?
Also provide your full sender name. Better if you post the full email you received from Zimbra, including all headers.
Also provide the full bounced message, including all headers.
Sounds like maybe the problem is how SPF/DKIM/DMARC are setup aren't matching how email was sent to Exchange.
In other words, the IP you used for mail initiation for mail sent to Exchange is blocked by your SPF/DKIM/DMARC setup.
Likely your Exchange logs will be helpful, as your logs will tell you exactly why Exchange refused to accept your mail submission.