I have my doubts. The sheds you showed us are characteristic of a antler degrading buck, i.e. one that's losing antler development as he ages. That might be true if the sheds came from an aging buck. But, like OK has posted, the only way to be sure is to do DNA testing.
As far as a breeding buck, or his off spring, traveling/wandering 13 miles that's not unheard of either. Migratory herds are well known to travel further than that. Younger bucks have been known to disperse that much and more.
Heck, where I hunt, one of the radio collared does went over 30 miles in a matter of a month, or less, when her water supply dried up. She was in her third trimester of her pergnancy. No known water as she crossed a rugged, very hot desert mountain range. After she settled in her new home, she gave birth to two healthy fawns. E
