موكلتي is the assignor who assigns someone else. The person who speaks is the assignee.

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Note added at 21 mins (2016-04-10 13:12:10 GMT)
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I have married to you my assignor in accordance with the dowry we agreed to and pursuant to the way of Allah and His Messenger.

in the first answer or translation there is a very serious mistake Islamically , the verb must be in the past tense it cannot be in different form otherwise it is a promise to marry him his client : I marry you my client is very wrong / it should be : I married to you OR I've married to you my client and the name of the lady must be mentioned in complete form , and the husband replies in the past tense as well nevertheless some scholors approves the response of the husband in present form but to avoid any SHUBHA he should say : i accepted this marriage
witnesses must witness assignment from the lady to the assignee and the rest of all the terms of the contract to isalmicaly valid .

Give in marriage is more accurate than 'marry' (see example)
Principal is the person who authorise someone in their behalf, the agent here is not paid, he's not her 'client' (see 5.a of the link below)