English translation: shall pay on behalf and to the order of
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Explanation: if you used to the order of, you have a serious mistranslation problem.
por cuenta de = for account of (banking/finance jargon for to be charged to the account of/at the expense of). It is sometimes translated as on behalf of, but in many contexts real bankers prefer for account of.
por orden de = by order of - exactly the opposite of to the order of.