In Outlook on the web, in the left-hand folder navigation bar, right-click on Inbox and select Permissions.
Click the + sign.
Type in the email address of the account you want to delegate permissions to.
Click Add.
Customize the permission level according to the access that the other person needs.
Click Ok.
The person you are sharing your mailbox with may need to refer to the KB article on Adding Shared Mailbox on Outlook 365 Desktop and Web in order to gain access to the newly delegated mailbox.