Here, you are speaking of "the faith OF Christ" (I think I posted about Galatians 2:20 in either this thread or another), but this is always (in Scripture) distinguished from "their/his/her" faith. So what we see in verses like Romans 3:22 is that distinction:
"22 Even the righteousness of God which is by [means of] faith of Jesus Christ unto all and upon all them that believe: for there is no difference"
Galatians 2:16 [ylt] -
"having known also that a man is not declared righteous by works of law, if not through [by means of] the faith of Jesus Christ, also we in [into/unto] Christ Jesus did believe, that we might be declared righteous by [/in] the faith of Christ, and not by works of law, wherefore declared righteous by works of law shall be no flesh."
"22 Even the righteousness of God which is by [means of] faith of Jesus Christ unto all and upon all them that believe: for there is no difference"
Galatians 2:16 [ylt] -
"having known also that a man is not declared righteous by works of law, if not through [by means of] the faith of Jesus Christ, also we in [into/unto] Christ Jesus did believe, that we might be declared righteous by [/in] the faith of Christ, and not by works of law, wherefore declared righteous by works of law shall be no flesh."