Kishimoto did not explain how exactly Kakashi possessed this rikoudo power but i have a new theory to explain it To you
When obito came as back spirit he was basically was Obito’s chakra and I think what happened was that obito hold in some of the juubi’s powers ( which partially explains how he was Use and able to kamui from the other dimension but not come fully) so when he gave kakashi his eyes he also gave him his chakara leading up to the juubi’s ultimately leading up to hagoromo sage of six paths chakra. That’s the only logical explanation to how kakashi even has hagoromo sage of six paths power in the first place.”Kakashi got both of Obito’s eyes.
When Obito basically infused his spirit with The Kakashi like the Sage did with Naruto and Sasuke. Then Kakashi received both of the eyes. The full power can only be use when they are together that’s why Obito couldn’t normally use Susanoo. Kakashi used all Obito’s chakra though so he lost the abilities later Fight With Kaguya Ōtsutsuki. And you don’t have to be brothers to have eternal mangekyou sharingan. You just need two Mangekyo sharingan. And to be fair Madara just take Kakashi’s eye out and eject it into his own so no reason Kakashi can’t just magically transform his own eyes with chakra.