No, you need to prove that this is your mom actually. There is an instruction on USCIS website. It lists all the required documents and the replacement of the documents if they are not available. You should follow the instruction and submit all the documents. You can also file online and scan the documents.
Bellow is from the instruction .
What Evidence Must You Submit?
You must submit all evidence requested in these Instructions with your application. If you fail to submit required evidence, USCIS may reject or deny your application for failure to submit requested evidence or supporting documents in accordance with 8 CFR 103.2(b)(1) and these Instructions.
Unless specifically noted otherwise, you must submit each of the documents listed below for you and your U.S. citizen parent through whom you are claiming U.S. citizenship at the time of filing to avoid delays in processing your Form N-600. USCIS may require verification for any or all information provided with Form N-600. Additionally, if you are scheduled for an interview with USCIS, you must bring in documentation if information has been updated or has changed after filing.
NOTE: “You” and “your” in this section refers to the individual for whom a Certificate of Citizenship is sought. It is NOT the applicant’s parent or legal guardian who may apply on the minor child’s behalf.
1. Photographs. You must submit two identical color passport-style photographs of yourself taken within 30 days of filing this application. The photos must have a white to off-white background, be printed on thin paper with a glossy finish, and be unmounted and unretouched.
The two identical color passport-style photos must be 2 by 2 inches. The photos must be in color with full face, frontal view on a white to off-white background. Head height should measure 1 to 1 3/8 inches from top of hair to bottom of chin, and eye height is between 1 1/8 to 1 3/8 inches from bottom of photo. Your head must be bare unless you are wearing headwear as required by a religious denomination of which you are a member. Using a pencil or felt pen, lightly print your name and A-Number (if any) on the back of the photo.
2. Your Birth Certificate. You must submit a birth certificate or record issued and certified by a civil authority in the country of birth.
3. Birth Certificate or Record of Your U.S. Citizen Parent. You must submit a birth certificate or record of your U.S. citizen parent issued and certified by a civil authority in the country of birth.
If your U.S. citizen parent applies, your U.S. citizen parent must submit his or her birth certificate or record issued and certified by a civil authority in the country of birth.
4. Marriage Certificates of Your U.S. Citizen Parent. You must submit a marriage certificate issued and certified by a civil authority in the state or country of marriage.
Form N-600 Instructions 02/13/17 N Page 8 of 13
5. Documents Showing the Marriage Termination (if applicable). You must submit a certified divorce decree, death certificate, or annulment document.
6. Proof of U.S. Citizenship. Examples of this are birth certificates showing birth in the United States; a Form N-550, Certificate of Naturalization; a Form N-560, Certificate of Citizenship; a Form FS-240, Report of Birth Abroad of United States Citizen; or a valid unexpired U.S. passport.
7. Proof of Status as U.S. National (only required if you are claiming U.S. citizenship through a U.S. national, such as a person born in American Samoa or Swains Island).
If you were born outside the United States or its outlying possessions, you are born a U.S. citizen if your parents met the following conditions:
A. Your U.S. citizen parent was physically present in the United States or one of its outlying possessions for a continuous period of one year prior to your birth; and
B. Your other parent was a national, but not a U.S. citizen.
NOTE: If you have a U.S. citizen parent and a noncitizen parent who is an alien but not a national, your U.S.
citizen parent must have met the physical presence requirements prior to your birth.
8. Proof of Legitimation (only required if you who were born out-of-wedlock and your father is your U.S. Citizen
For information regarding legitimation see the USCIS Policy Manual at
Provide legitimation documentation from the country or state in which you legitimated. Legitimation can also be
established according to the laws of your father’s residence or your residence.
9. Proof of Legal and Physical Custody (only required for applicants whose U.S. citizen parents divorced and/or
separated and for applicants who are adopted or legitimated).
10. Copy of Permanent Resident Card or Other Evidence of Permanent Resident Status (only required if you are
claiming U.S. citizenship after birth through a U.S. citizen parent).
11. Proof of Required Residence or Physical Presence In the United States. Any document that proves the U.S citizen parent’s residence or physical presence in the United States. This proof may include, but is not limited to the following:
A. School, employment, or military records;
B. Deeds, mortgages, or leases showing residence;
C. Attestations by churches, unions, or other organizations;
D. U.S. Social Security quarterly reports; and
E. Affidavits of third parties having knowledge of the residence and physical presence.
12. Copy of Full, Final Adoption Decree (only required for adopted applicants).
13. Re-adoption in the United States. If you had to be re-adopted in the United States, submit evidence of a full and final foreign adoption if the appropriate authority in the applicant’s current location of residence recognizes its validity.
14. Evidence of All Legal Name Changes. If you legally changed your name, submit evidence of an issued and certified document by the court that authorized the legal name changes.