If someone overstayed visa for seven years and married a PLR, would that person be able to work after 1-130 is approved?

When a person marries a LPR or a US Citizen, that person is eligible to adjust his/her status, i.e. get a green card. The application process can be completed in two parts. First, sending an I-130 petition for alien relative (to prove eligibility) and then, form I-485 with accompanying documents and forms. During the second part, an applicant sends its I-765 to apply for work authorization and a social security number. Now, once the I-130 petition is approved the applicant can only move forward with the application. This means that at this point there is still no work authorization. That said, it is worth noting that the law understands that a person must work to live, accordingly form I-486 asks if a person has worked without authorization. Now, considering the question, if a person overstayed his/her visa, a waiver of unlawful presence is necessary. Once that waiver has been approved, a petitioner can move to the second part of the petition for a green card.