Sync deleted emails with Gmail

[Wojciech Żuk]

Hi,
I have problem, I use Gmail to collect e-mails from my 3 external accounts.
So I created fo every account in gmail labels with accountname\Inbox
accountname\Sent and every of these folders are synchronised two-way
without problem.
Problem is with deleting email, when I delete message of any on my external
account using mail client (thunerbird, outlook), after synchronisation
message is deleted from it's corresponding folder name on Gmail, but it
stay in Gmail\All Mail.
Because on Gmail only messages moved to Gmail\Trash are truly deleted.

I don't know how to resolve this problem, resolution could be to move Trash
messages from these three accounts but only one way and append (not delete
exsisting) it to Gmail\Trash. Then deleted messages on e-mail clients would
be also deleted from Gmail\All Mail.

could anyone help with that?
thanks
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