There are great options for who marries a US citizen because in that case the green card is given earlier. The priority processing time is given to such cases. The time processing of the green card is high for spouses of those candidates who are just PR holders in this country rather than having citizenship.
Since your daughter is marrying someone who has a green card of this country, she is also eligible for getting the green card but then the processing time is high. So, she can wait for some time, when her husband gets the citizenship of US and getting the green card will be faster for her then.
Your daughter is eligible to fill the form I-130 right now when her husband has the green card or in the future. She can only file the I-130 form when her husband is the green card holder after marrying him. As his fiancé, she can’t file the form, I-130 because he is just a green card holder and not a US citizen. Only US citizens are eligible to sponsor their fiancés for a green card.
Filling the form I-130 now
The candidate can get the complete information about this form(I-130) through Nile Migration. The candidates after filling this form, are allotted a priority date. At this date, they have to give an interview at a US consulate. The form I-130 can be filed from the home country also instead of US, by sending it to the USCIS office located in Chicago.
When you want to file the alien relative immigration petition(form I-130 from the US)
In case, the marriage has taken place outside the US, a K3 visa(spouse visa) is needed to get to the US before you obtain the green card. This visa is a non-immigrant visa.
However, since the candidate might marry the US green card holder after entering the US, the process is different. In that case, the candidate needs to get the US fiancé visa(the K1 visa) from the home country and then enter the US.
The candidate gets the approval for his I-130 form from USCIS after which he is allotted a case number at NVC. The USCIS shifts the case to NVC. To get this interview scheduled, the candidate has to pay a designated fee amount, but this fee payment does not happen at NVC. In fact, the candidate gets to know through NVC where this fee payment should be done.
After this fee, the candidate has to provide another form for his immigration visa application(DS-260) after which the interview is fixed. Prior to this interview, the candidate has to provide his necessary documents to NVC either via email or courier. At the interview, he has to bring his form submission receipt. The interview contains exploratory questions from a candidate asked by a visa officer.
The NVC only schedules the date of the interview. This interview does not happen at NVC but at a local consulate. Before this interview, a medical checkup is however necessary. In India, the US embassy at Delhi and Mumbai are authorized to take such interviews.