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Every incoming e-mail is filtered by some e-mail filter rules, based on a language called Sieve.
E-mail filters rules include: vacation, forward, spam filters, general filter rules. These 4 points (your main filter settings included) can be managed using the webmail interface of Horde. The old one, based on Procmail, is now disabled.
All e-mail clients (pine, thunderbird, etc.) filter rules work after the rules managed through webmail service (horde), so any e-mail client can not overwrite or overtake the rules fixed/managed through webmail service.
If you define a rule through webmail service, this will be active until when you change or overwrite it. The activated filters are the ones which have been saved for last.