I would use them and see if the government attorney objects. Rules of evidence are relatively relaxed in most Immigration Courts. Hopefully you have an attorney working on your case, you should never go through removal proceedings without an experienced immigration attorney.
It is up to the judge to decide if he/she will accept them.
Are you on the respondent's 'side' or are you hoping that he/she will get deported?
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Respondent need an immigration lawyers and soon. Removal proceedings are way too complicated an endeavor to be handled on your own. I will assure you, this is not the first question you will have on your way to the final outcome of your interaction with the immigration court system.
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The issue is whether the evidence is relevant and reliable. It appears that you would be able to establish the relevancy of the emails, since you indicate they would essentially counter the government's claim of fraud. The issue of the reliability of the evidence, which is hearsay, is where you need to focus. I would suggest that you submit the evidence along with a short brief outlining the admissibility of the emails. It would be helpful to also submit something from the email provider corroborating the authenticity of the emails. For instance, contact gmail or yahoo or whatever the provider company is and ask if they can provide any documentation verifying the email sender, receiver, date, etc. Finally, if you submit the evidence in a timely manner (usually 15 days before the hearing), and the government does not file a timely objection, you can argue that the government waived its right to object by not doing it in a timely manner as required by the immigration court's Practice Manual.