Is it permissible to transfer the remains of a father to a private family cemetery after one year of his burial in the public family cemeteries, in order to fulfill his wish of building a private burial place?

It is not permissible to exhume graves except out of a sharia-compliant necessity, and the father's wish to be buried in a family-specific cemetery does not justify exhuming his grave after he has been buried in another cemetery. What benefits the deceased most is seeking forgiveness for them, performing righteous deeds, and dedicating their reward to them.