Molson said it was a priority in 2016 for the Canadiens and general manager Marc Bergevin to find an established, long-term leader.
"The first step in that process was to get Shea," Molson said. "We gave up P.K. to do that. You've seen the past [five] years how things have unfolded. One of Marc's biggest priorities was to get a leader who would be with the team for many years and guide it to success."
The Predators selected Weber in the second round (No. 49) of the 2003 NHL Draft, and Nashville GM David Poile recalled how difficult it was to trade Weber, then the Predators captain, to the Canadiens for Subban, who had won the Norris Trophy voted as the top defenseman in the NHL in 2013.
The Predators traded Subban to the New Jersey Devils on June 22, 2019.
"Think of Shea in terms of how he developed and matured as a player and eventually became our captain," Poile said Sunday. "If you're asking me to name three or four players who were the face of our franchise, who have done the most to make the Predators successful, Shea would be right there at the top of the list.
"He has a presence. It's obvious on the ice. He's become one of the best defensemen in the League, his shot is the hardest in the NHL, and he plays a very physical brand of hockey. What's not to like? It's pretty hard to criticize Shea Weber as a player.
"Off the ice he carries himself very professionally. He's a very proud man. His legacy will always be very, very important for what he did for hockey in Nashville, establishing the game, and also for his presence in the community. He's a very generous person and a very popular player."
Weber (6-foot-4, 229 pounds) is the same height and 4 pounds heavier than the listed height and weight for Larry Robinson, the Hall of Fame defenseman who played for Montreal from 1972-89. Robinson's 1,202 games are the most by a Canadiens defenseman.
"Shea's become a complete player," Robinson said. "The first thing I like about him is his shot, which is a cannon."
Weber has won the Hardest Shot contest each of the past four times it's been held as part of NHL All-Star Weekend.
"And he's become a very, very good defender," Robinson said. "Shea has transitioned from the old game to the new game very, very well. A defenseman today has to be more mobile than in my day. You've got smaller, stronger skaters now who are coming at you at 900 mph. You can't hook and hold or interfere with them at all. It's so much more important now to have body position and to always be thinking ahead of where the play is going.
"As captain he doesn't have to say much, like Henri Richard didn't in my time. Shea's there, he sticks up for his teammates, he comes to play and to work every night. The players look up to him, and when something has to happen, he's usually front and center."
Chelios, co-captain of the Canadiens with Guy Carbonneau in 1989-90, said Weber has much left to accomplish in his career. But he did point out one record that may be out of his reach.
On Tuesday, Weber will be 651 games shy of tying Chelios' mark.
"I love the kid, and my congratulations to him for 1,000 games, but good luck with that," Chelios said.