I believe it was the words "your kingdom" that saved him.
He believed Jesus was who He said He was and actually HAD a kingdom, and that there is some kind of consciousness there and the repentent theif wanted Jesus to remember him.
As I understand scripture and many evidences in my own life and the many testimonies of my brothers and sisters ... Jesus' love is very easily given and all we have to do is believe Hin and receive Him.
If you’ve ever been with an individual going through the death process there are amazing things going on between them and the Lord.