Export Exchange 2013 mail users?

Please configure export permission for the user as commented by Saif
You can add the Mailbox Import Export role to the Organization Management role group. Or you can create a new role group, assign the Mailbox Import Export role, and then add yourself as a member. For more information, see the "Add a role to a role group" or the "Create a role group" sections in Manage role groups.
Below is the example to add the Mailbox Import Export role to the Organization Management role group. By default, the admin is the member of the Organization Management role group.
In EAC, navigate to permissions> admin roles> Organization Management>Edit> Roles:Add> click Mailbox Import Export> add> OK> Save.



If that did not work you can assign using the following command from Exchange Shell. Replace exportadmin with your user.

New-ManagementRoleAssignment –Role “Mailbox Import Export” –User exportadmin

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And run the following command to export. Replace john with the user you wish to export.

New-MailboxImportRequest -Mailbox john -FilePath \\HQ-FS01\PST\john.pst

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Please check this article to export in bulk.
https://www.experts-exchange.com/articles/16179/Export-mailboxes-to-PST-one-by-one-in-Exchange2007-and-2010.html

Hi Saif, thankyou. When I choose Export to a PST file I get two choices:
- export only the content of this mailbox
- export only the content of this mailbox's archive

what is exactly the difference?
Thank you!

I read this:
https://docs.microsoft.com/en-us/office365/servicedescriptions/exchange-online-archiving-service-description/archive-features
my guess is that I need to select:
export only the content of this mailbox
correct?