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The only way to close that fake account is reporting it to Facebook. But, for that, you need that profile page. Either you can find the person by searching on the facebook or ask your friend, to send you the link of the fake profile. So, that you can report it. It is very difficult to do this on iPhone or iPad, it will be best to do this from any computer.
If you have any computer present in front of you then, I can directly connect with it and help you to do this job.
Here is the steps to report the fake profile.