[Users] Processing rules on folder without opening it?

[Victoria Stuart (gmail)]

I have various email accounts, each with an Inbox and a processing rule (filter: all new mail move to another folder ...).

I want to automatically move the messages that arrive in those Inbox folders to a default Inbox (my main email account), without first having to click those various Inboxes (to trigger the filter). 

How can I accomplish this?

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