You want to give a user permission to a mailbox.
The Add-MailboxPermission cmdlet handles this without much fuss.
Add-MailboxPermission -Identity "johndoe@evilcorp.com" -User "Admin" -AccessRights Full -InheritanceType All
This example gives “Admin” FullAccess rights to the johndoe@evilcorp.com mailbox.
I have made the mistake of swapping the target mailbox and the user who is being given permission. The purpose of this recipe is to explain it in plain language as a reminder to myself.
-Identity is the target mailbox-User is the user being given permission to the target mailbox