Caron played alongside the late Hall of Famer on the Lakers from 2004-2005 ... and the two remained great friends up until the legend's tragic death in 2020.

The 2011 NBA Champ says Bryant -- who had a series of children's books of his own -- once gave him pointers on how he could use his authenticity to motivate the next generation ... which led him to write "Shot Clock," alongside Justin Reynolds.

"He did like a little moment with me prior to him passing," Tuff Juice tells us. "We connected and we talked about the writing process and how it's so tough to be authentic and clear and real, but it's exactly what the kids need."

"He always told me to 'Tell your truth, be brave and people gonna accept it or reject it, but be brave in that process,'" he added.

Butler says he made a promise to Kobe that his second act would be "far better, more profound" than his playing career ... a vow he also disclosed with Bryant's wife, Vanessa.

The book is deep ... and reflects what Caron really went through in life -- from traveling the world to run-ins with law enforcement and losing friends to gun violence.