In a hybrid Exchange Server environment, remote mailboxes are not shown when you try to configure email forwarding for a mailbox in Exchange admin center (EAC).
The filter that's used for searching the remote mailboxes is missing RemoteUserMailbox under RecipientTypeDetails.
To fix this issue, install one of the following updates:
For Exchange Server 2019, install the Cumulative Update 7 for Exchange Server 2019 or a later cumulative update for Exchange Server 2019.
For Exchange Server 2016, install the Cumulative Update 18 for Exchange Server 2016 or a later cumulative update for Exchange Server 2016.
Learn about the terminology that Microsoft uses to describe software updates.