Hi @exchange beginner ,
Based on my knowledge, "Search-mailbox" cannot specify a folder, so it cannot meet your needs.
1.You could following the steps export inbox of source mailbox to .pst file, then import the .pst file to target mailbox.
Export: Outlook client -> File -> Open&Export -> Import/Export -> Export to a file -> Outlook date File (.pst).
Import: : Outlook client -> File -> Open&Export -> Import/Export -> Improt from another program or file.
For more information: Back up your email

2.You could assgin “Full access” permisson of target mailbox to source mailbox. Log in to the source mailbox in the Outlook client. Then select the Inbox folder of the source mailbox, then hold down the "Ctrl" key and press "A" to select all mails. Then right-click and select to move to “Taget mailbox”. After that, I can view the mail in the inbox of the target mailbox.

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