Before considering whether the naturalization application will be approved, he should ensure he is not inadmissible due to CIMT. I cannot stress enough, in this case, how important it is to have the case reviewed by an experienced immigration attorney.
This response is general in nature and cannot be construed as legal advice, given that not enough facts are known. Any comments offered on Avvo are of a general nature only, and are not meant to create an attorney-client relationship. If you would like additional information based on this response, please contact my office at 510 657 7665 or 415 902 0832 to schedule a consultation.
Do not file for anything before consulting privately with an attorney. The USCIS has the discretion to consider the crimes committed and likely will. In addition, depending on the sentence, your cousin may be deportable. Your cousin should speak to an attorney in his area. I'm located in Alexandria, Virginia.
The answer provided is for general information purposes and cannot be relied upon. In order to provide legal advice, one must engage with a live attorney; this answer does not create such attorney-client relationship.
One is subject to removal for 2 CIMT's, he should file nothing if he wants to stay in the U.S.
The above is intended only as general information, and does not constitute legal advice. You must speak with an attorney to discuss your individual case.