The basis of the Reaper death seal is to seal both the user and the victims souls with in the shinigami for eternity.The tailed beast are living containers for the Chakra the SO6P spilt from the Juubi with the creation of all things jutsu. Kurama's Yin chakra was intertwined with Minato when he sealed his soul into the shinigami..He states that the chakra is heavy and gets his body numb.
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As u see in the panel before he performed the 8 trigram seal to only transfer the Yang chakra in to Naruto his soul and Kurama's Yin chakra were intertwined together meaning that both his soul and Kyuubi chakra are trapped together for eternity..Now since his soul has been released from the Shinigami why would only Minato's soul be released and not Kurama's chakra when they were both intertwined and sealed together? Oro's hands are a part of his soul so hindsight it's a part of his soul that was missing.
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Many people have been debating and arguing when the facts are clearly in the manga it's not a assumption or theory it's there in the chapters.Thats why i strongly believe what Minato will be giving his son is more then jus a hug, fatherly advice, fighting along side him or whatever theories are thrown out there..
Plain and simple Minato has sensed Naruto and Kurama are a team and his son can handle Kurama's full powers and abilities..Hence why the gift is the other half of Kurama's chakra. Being knowledgeable with Uzumaki sealing jutsu's he can unseal the chakra trapped inside his soul with out dieing since he is Edo. His body can hold the chakra strongly now that he has Zetsu body as a vessel which is made of Hashirama's dna. For those that ask why Hiruzen sealed Edo Hashirama & Tobirama and their souls are intertwined..Simple Hashirama & Tobirama were living people.How would only Minato's soul be released and within his soul the Yin chakra is bonded since it's jus energy it's not a soul.
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