Once you've been added as a delegate to another mailbox, tap on the Add Account button in the sidebar and then tap on Add Shared mailbox on the menu that pops up. This will start the account addition process.
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You can also go to your account settings, and then tap on Add Account. Then tap on Add Shared mailbox on the menu that pops up. This will start the account addition process.
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Enter the alias of the mailbox that you have been granted access to. This should add the mailbox to your existing set of accounts.