Although the formal announcement of Moylan's arrival at the Sharks and James Maloney's departure to Penrith has not yet been made, Graham said the players were all aware of it.
Moylan could potentially be Cronulla's best player, according to Graham.
The player swap brings an element of sadness to see another member of the Sharks' 2016 premiership-winning spine leave, after fullback Ben Barba (rugby) and hooker Michael Ennis (retirement). But Graham, who played a couple of under-20s matches with Moylan at the Panthers before leaving at the end of 2010, at least knows the quality Cronulla are getting with the former NSW and Australian player.
"He's a good fella, Matty, and he's going to be fine," Graham said from the Australian team hotel in Manly, which he is sharing with Maloney as members of the Kangaroos World Cup squad. They have both been named in the 17 to play Lebanon on Saturday night.
"It will be a bit of a change… 12 months ago you'd never thought Matty was going to leave Penrith. But sometimes things don't pan out, you go somewhere else and things happen. Look at Lewie (Luke Lewis). He had to leave Penrith and a few years later he wins a comp. You just never know what's around the corner."
Moylan, 26, is expected to sign a four-year deal this week with the Sharks while 31-year-old Maloney is being offered a three-year contract at Panthers.
Graham was unsure where the Sharks will put Moylan – a representative five-eighth and fullback.
"That's a question best for Flanno (coach Shane Flanagan), not me," Graham said.
"But one thing I do know with Flanno is that it's not necessarily about positions. His philosophy is get your best 17 players on the park [and] just make it work.
"But obviously there'll be a few big decisions down there next year on the back of Duges (Josh Dugan) coming in, Matty, Jimmy going. I know Matty played No.6 at Penrith but he's only new to the position."
Graham said Moylan's talented ball-playing and weaving runs were spawned by taking a break from rugby league at high school to play touch football.
"That was the best thing for him," Graham said.
"That's where he got all those skills from, touch footy. He came back to league and kept kicking on, kicking on, with those silky skills.
"I feel like he'll really fit in, to be honest. It's no secret that probably the last six months haven't been the best for Matty with the off-field and on-field stuff.
"We've all been through that in our career but it does settle down. He's still playing good footy. But he got the (hamstring) injury and that disrupted his rhythm and then stuff snowballed off the field so it wasn't the best.
"Once he settles back into some tough work and playing footy, he'll come forward a better player. It's amazing when you come through a tough period… and he's too much of a talent not to come through. He can easily be the best player in this (Sharks) team, the best player on the field at any given place."
Don't be fooled though. Graham is going to miss Maloney, especially his goal kicking, which hovered above 80 per cent accuracy right through 2017.
"I might have to put my hand up!" Graham said.
"Look, I know Jimmy was a special kicker… but Val [Holmes] kicks when Jimmy isn't playing and I remember seeing Matty kick goals from the sideline for Penrith to win games. Chad Townsend used to kick as a junior so goal kicking is the least of our worries.
"But we'll miss Jimmy, he's a real character. As much as he drives you bananas, he's good for a laugh too. And his ability on the footy field, you can't question.
"Look, what he's done at clubs – the Warriors, Roosters, us. He's been to three Grand Finals. He's now a Test player, the Origin five-eighth. He's certainly going to be missed. There's a definite hole there we have to work on like we did with Micky Ennis. That's the first hole. Jayden [Brailey] stepped up and is doing a great job but has still a way to go."
Graham has been working hard for Australia and will play his third consecutive Test this weekend when Australia face Lebanon.
Asked how he ended up such a rugged back-rower when he grew up with three sisters, he said: "They are the reason I am like that. You had to defend for yourself out there!
"I love my sisters. They kept me in check and weren't afraid to hit me with the truth."
Graham's two elder sisters have two sons each, which means Uncle Wade's four footy-mad nephews will all be at Allianz Stadium on Saturday. And who knows how many tries Graham might grab after his four against France in Canberra.
"I'm not really known for my try-scoring feats so it still hasn't really sunk in. It was just one of those nights when I was in the right place at the right time – four times."