Glad to see you could migrate mailbox to Exchange on-premises and could use it in OWA successfully.
About client access, in a hybrid organization, if there still exists mailbox on the Exchange on-premises, you need to point the Autodiscover record to the Exchange on-premises.
Otherwise, this mailbox will cannot be used in Outlook. Because the Outlook client needs to use Autodiscover to configure profile. OWA doesn't need to use Autodiscover.
Here is a blog which may be useful to you: Office 365 Autodiscover Lookup Process
Please Note: Since the web site is not hosted by Microsoft, the link may change without notice. Microsoft does not guarantee the accuracy of this information.
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