From Halopedia, the Halo wiki
Michael James Cole was a brother of Admiral Preston Cole. Of his six siblings, Preston appears to have been closest to Michael, judging by the fact that he wrote to Michael throughout his military career. In 2489, Preston wrote to Michael asking him and his wife Molly to join him in the Outer Colonies.
Michael James Cole is not to be confused with Michael H. Cole who acted as witness to Preston's wedding ceremony. Since their father's name was Troy, and it is highly unlikely that two siblings or even cousins would have the same name, Michael H. Cole was almost certainly Preston and Michael's grandfather or uncle, and the younger Michael was likely named after him.
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