Wrong DoB on my mother's passport

[neo5167]

Hi,

I am applying for a greencard for my mom. Her DoB is wrong on the passport and her US visa. We contacted the passport office several times and they refused to change the DoB on the passport. My question is what will happen if I apply for her greencard with DoBs different on birth certificate (date x), 10th certificate (date x) and passport/visa (date y). What is the correct procedure I must follow before applying for her I485?

Thanks!