it is permissible for the son to marry the sister of his father's wife who is not the sister of his mother but the sister of his mother's co-wife as mentioned in the question. The basic rule is permissibility as long as there is no reason to prohibit it.
(Part No. 18; Page No. 371) it is permissible for her sister to bring up that son but she is not allowed to adopt him as her own son. The adopted son will not be eligible for inheritance from his adoptive parents. May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.