No. When you file your I-751, the status automatically prolongs, as a permanent resident you do not need a work authorization card to prove you can accept employment.
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No. Under the Code of Federal Regulations, an I-751 petition must be accompanied by evidence of a valid marriage, such as evidence of commingled finances, joint ownership of property, etc. But your petition does not require the filing of a new I-756.
The above information does not constitute legal advice, and is intended only as general information. You should speak with an attorney to discuss your individual case, as not all facts are known at this time.
No work authorization is required.
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.