sent emails copied with outlook rule are not synchronized on gmail

Occasional Visitor
Hi,
 
i have a problem with imap gmail sync, i have 2 different accounts on outlook 365 app:
gmail and my pop3 libero.it
I created a rule on outlook that copies the mails sent from libero.it into the sent mail folder of gmail, this works, but then it is not synchronized on the gmail server and I do not see it in webmail,
 
but, f I copy the email sent by libero.it without automatic rule (manually), this email is copied to Gmail at imap synchronization, why?
 
thk
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