Hello @EllaM3 ,
Wordpress tends not to allow outside scripting, otherwise I'd recommend having your client use the archive tool. In all honesty, the best way for them to do what they want, would be to manually hyperlink the scheduled / sent emails' share URLs directly to the site. Keep in mind that until the email is actually sent, the link won't be live and accessible, but the URL will generate the moment the email is at least scheduled.
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