If there is an entry stamp in her passport (although not very visible), she should make a copy of it and submit it with her adjustment of status application. She should also take her original passport to her interview, so that USCIS can verify her lawful entry.
In order for immediate relatives to become legal permanent residents, they must demonstrate legal entry. Whether your mother can demonstrate legal entry will be determined by the Immigration Officer at the interview.
If you have specific questions about the processing of your case, do not hesitate to schedule a consultation with my office.
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Elizabeth R. Blandon
Lawful entry can be established by alternate means if the entry ccard and stamp are not available. For example, we have used passports of persons who traveled with the person, statements from the persons someone traveled with or who picked them up at the airport, boarding passes, visas showing the person had a valid visa on the day she entered, etc.
The biggest concern here is the fact that, according to your question, Immigration cannot find any record of her entry.
We would be happy to assit you with this.