If you say that 'the manager has taken the matter up with the board of directors' you are emphasizing that it just happened -the recentness of the event, that it may or may not have been reviewed yet. It is continuing, so it is the present perfect of 'to take'. If you say 'the manager took the matter up with the board of directors' you put weight on the fulfillment of an action in the past -it's the past tense.
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