Setup the 'From' Field in Outlook
You have access to the mailbox, so it is most likely that the 'From' option is not enabled in Outlook. To enable this feature, please follow these steps:
Open up a new email
Go to options -> the 3-dot menu and select the 'From' option
This will create the 'From' option
You can then use the drop-down option on the 'From' field to select the mailbox that you want to send from.
I will leave this ticket open for a few days, in case this is not the problem you are experiencing. Just respond to this email if you require any further assistance.
Regards,