How long will it take for a fiancé to get permanent residence in US?

probably 3-4 months after they marry and file an I-485.

Once your brother's fiance arrives in the United States, she will be processed and admitted. She then has up to 90 days to get married to your brother.

Once they have become husband and wife, they'll have to file for Adjustment of Status. The following forms are needed for this:

I-485 (AoS),

I-864 (Affidavit of Support),

2 x G-325a (biographic info for both of them),

I-765 (work permit—EAD), and

I-131 (Advance Parole—AP).

The latter two are optional but free of charge when submitted with the package, so that's the way to go as it gives her a nice plastic card which is a federal photo ID.

Also needed is a check for $1,030. Personal check is okay and actually preferred and preferred as it allows to trace when it was “cashed.”

After about 10 to 12 weeks she will receive a plastic card which now is a combination of work permit (EAD) and Advance Parole (AP). At about the 3 to 5 months mark, she will receive her “conditional,” 2-year Green Card. Most AoS petitions based on a K-1 (fiance visa) do not have an interview.

She has to enter the US within 6 months. When in that time frame is up to her.

They have to marry and then apply for AoS within 90 days of her entering the US. When in that time frame is up to them.

She will be a PR within 6 months after they are married and file for AoS.

10 to 12 weeks approximately.

http://www.visajourney.com/content/guides