There is no mechanism in Exchange to allow access to external users. You will have to create a mail user object for them in your own directory in order to be able to delegate access (and assign a mailbox too, depending on the type of access you require).
shared mailbox access
Glenn Maxwell
11,521
Reputation points
Hi All
i am using exchange 2016 hybrid envrionment. I have a shared mailbox created in onprem and migrated to online. I have a requirement to provide access to this shared mailbox to couple of external users This external users are not in my domain. If i create a mail contact for these external users and provide access to shared mailbox, will they access the shared mailbox?