Connect-Mailbox is used to connect disconnected mailboxes to existing user accounts that don't already have mailboxes.
If you are looking to extract data from the mailbox and delete it, then you can export it to PST either using outlook or Exchange management shell/ECP. Once done, import the PST to the user mailbox who needs that data.
If you would like to keep both mailboxes, you can assign Full access permission for the user who needs it to the other mailbox. In this way, user will get the target mailbox added to the outlook profile and can access.
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