sent emails copied with outlook rule are not synchronized on gmail

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