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You could also have them select the person and then submit the form and use a workflow to move those items over quite easily. Actually would be easier than trying to do this within the form itself.
you can add a lookup control on the form that quries from the same list the form is designed for, and set up a filter to filter by current user
Thank you! This is exactly what I was looking for. I completely forgot that I can use a List Lookup control directly from the form.