In a Hybrid Scenario, recipient management is handled on Premise and then synced to Azure AD.
Rights of Mailboxes are still managed online - Exchange Admin.
Due to Exchange no longer being installed On-Premise there is no TAB for email addresses under a users properties in On-Premise Active Directory.
You will need to enable the Advanced Features within Active Directory Users and Computers.
Once you have done this you can drill through the users OU's and find the user you want to add an alias for. Do not use the search (Find..) function as the Tab will not display in the users properties.
Right click on that user and choose Properties.
Select the Attributes Editor TAB.
Drill down until you find the Proxy Addresses field, highlight it and press Edit.
In the Value field enter the SMTP email address alias' you want to add. If you want that alias to become her Primary SMTP address then you must type SMTP in capitals otherwise just leave in lower Case.
e.g.
SMTP:firstname.lastname@domain.com (Primary email)
smtp:firstname.lastname@domain.com
Once completed you just need to wait for the changes to sync up to Azure AD. You can check it has synced by looking in the email address section for that user in Exchange online.
You can force an Immediate sync of AD to Azure by running the following PowerShell Command :-
Start-ADSyncSyncCycle delta
** NOTE : If you still cannot create this email alias then it must exist somewhere in the Active Directory - check Shared Mailboxes of offboarded users.