Hi, thanks for posting here in Microsoft community, it looks like delegated access between on prem and EXO mailboxes requires proper hybrid configuration. If an on-prem user can’t access an EXO mailbox, check the Hybrid Modern Authentication is enabled then then Autodiscover and free/busy sharing are working also the OAuth configuration between on prem and EXO is complete.
You may need to re-run the Hybrid Configuration Wizard and verify that delegation settings sync via Azure AD Connect.
Also, have you confirmed whether OAuth and Autodiscover are correctly configured for hybrid authentication? This is often the root cause of cross-premises delegation issues.
I hope this helps you, let me know how it goes.
Chard