Answer: If the student’s family gained permanent housing after the beginning of the current school year, the student has the right to remain in the school of origin for the rest of the year, if it is in his best interest. If the family gained permanent housing before the beginning of the school year, his status would no longer fall under the McKinney-Vento Act, and he would no longer have the right to stay in his school of origin or to receive transportation there. 42 USC 11432(g)(3)(A).
However, depending on your state, there may a state law that gives him the right to finish 12th grade in the same school. There also may be other ways for him to finish up his senior year at his former high school, i.e. open enrollment, an inter-district agreement, etc. I would recommend exploring those with the family to see if they can take advantage of them, and make the case that changing schools at this point in his school career would be disruptive.