US citizen and out of status alien marriage

What is the name of your state? California

I just got my citizenship and I want to marry my sweetheart and petition for her green card.
She came in US on a J1 visa, no 2 year home return requirement, then got out of status for about 2 years (she lived with me in US all this time) and she also worked all this time even if she had no work permit.
She filled and payed all her taxes, every year.

My questions:

Are we going to have any problems with getting a green card for her if she worked without authorization for all those 2 years ?

One friend told me that if I'm not a "born in US" american citizen she would not be able to get her green card and be forgiven for the fact that she worked without a work permit. And only a "US born" citizent as spouse will be able to help her out.
Is this true ?

Any help appreciated. We have a great relationship !

Please "IAAL" don't answer and/or reply to my post !
Please "IAAL" don't answer and/or reply to my post !
Please "IAAL" don't answer and/or reply to my post !

No, there is no distinction between a US born or a naturalized US citizen for purposes of sponsoring a spouse for permanent residence. First of all, you have to be married in order for you to sponsor her. Secondly, her J-1 must in fact not be the type that requires her to go home for 2 years to satisfy that home residency requirement. And third, she must be able to document that her initial entry to the US was a lawful one.

Please let me know if you have any additional questions or if I may be of further assistance to you in this matter.

Thank you Lana !