Summary of Law & Sengoku then
Sengoku fashback:
Rocinante reports to Sengoku about a child with amber lead syndrome joining the Family. He says the child hates the world, and reminds him of his brother when they were kids. Sengoku cautions Rocinante to not get himself too involved with the child, or you may expose your position.
Rocci acknowledges that and tells him he's here to stop Doflamingo from reaching Dressrosa.
Present day:
Sengoku tells Law about a marine who died on duty. He was someone special to Sengoku.
Sengoku knew the marine since he was a lad, and raised him like he was his own son.
He was an honest man with a good heart, and a reliable soldier… but he made single lie to me in his life.
Sengoku flashbacks to seeing the picture of deceased Corazon, and shedding tears at the death of Rocinante.
He realizes Rocci betrayed him for a reason.
There were four things lost on that day... "Barrels Pirates", "Life of one of my men", "Ope Ope fruit"... and the "Child with amber lead syndrome". He looks at Law, and Law answers yes, that child was me.
I see, as I guessed Rosinante abandoned his mission to save you. He took the Ope Ope fruit and died to save your life, is that right? Please tell me, I need to know how and why he died!
Law confirms Sengoku's words, and tells him he owes everything to Cora-san.
That's why he's lived his entire life to bring down Doflamingo.
But now that it's over, he doesn't know if this is the life of "D" Cora-san wished for him to live.
Law tells Sengoku that both he and the Straw Hat has the name of D, and asks him if knows anything about it.
But Sengoku refuses to answer his question, and lets him know Roci did not know either.
He tells Law that Roci didn't save him because he was a D. Don't attempt to give reasoning to the love you received from him.
Sengoku thinks to himself (So this man is a D as well... the Ds always ends up with a strange fate.)
Sengoku tells him if he was still an active marine, he'd throw Law into jail and have a long chat.
He gives final sage advice to Law, that if he wants to do something for Roci, then let's remember him in our memories. Live your life in freedom, Law, that's what he would have wanted you to do.