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Ben Affleck Is 'Slowly Getting to Know' Jennifer Lopez's Twins Max and Emme, 13: Source

Ben Affleck is spending time with Jennifer Lopez's teens as the pair rekindles their romance.

A source close to Lopez tells PEOPLE in this week's issue, on newsstands nationwide Friday, that her 13-year-old twins, son Max and daughter Emme (whom she shares with ex-husband Marc Anthony), are "onboard with starting fresh in Los Angeles," where Affleck lives.

The source adds, "They are slowly getting to know Ben. Everything seems to be running smoothly. It's very obvious that Jennifer is serious about Ben. She hasn't looked this happy for a long time."

Another insider recently told PEOPLE that Affleck and Lopez were "very affectionate" with each other during a family dinner together with Max and Emme at Nobu in Malibu.

The insider added, "Ben and her kids seemed comfortable together. The kids kept chatting with Ben. Ben seemed great. He was smiling and laughing. They ordered a lot of food to share."

Emma McIntyre/Getty (2) Ben Affleck (L); Jennifer Lopez

Jennifer Lopez / Instagram

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Rumors of Lopez and Affleck's rekindled relationship first began in late April when they were spotted outside her L.A. home following her split from ex-fiancé Alex Rodriguez. The two later enjoyed a getaway to Montana, where they were photographed driving together on May 8.

Since then, the previously engaged pair have been seeing each other in L.A. and Miami, where Lopez has her home base.

RELATED: Jennifer Lopez and Ben Affleck Are 'Starting to Talk About' Their 'Future' Together: Source

Affleck shares three kids with ex-wife Jennifer Garner: daughters Seraphina, 12, and Violet, 15, as well as son Samuel, 9. Speaking with PEOPLE in February 2020, Affleck said he and Garner, 49, have always made a point of being united for their kids.

"When you have children with somebody you're connected to them forever," the father of three said at the time. "And I'm very lucky she is the mother of my children."

"I'm very grateful and respectful of her," he added of Garner. "Our marriage didn't work, and that's difficult. Both of us really believe that it's important for kids to see their parents respect one another and get along, whether they're together or not."