How to address a child who's been stealing?

Assalamualaikum, everyone. I recently discovered that my neighbor's daughter has been shoplifting. We're both Muslim families, and she's close friends with my own daughter-they're about three years apart, both in elementary school. Subhanallah, they often play together, and Alhamdulillah, our neighbors are wonderful people, always kind and respectful. The other day, I took the girls to the mall and a couple of stores to have some fun. We offered to pay for the neighbor's daughter as a treat, since her parents are always generous with my daughter. But at one stall, my husband noticed her take something and put it in her bag without paying. At first, I wasn't sure, but later at home, I found several items she'd taken from every store we visited. Astaghfirullah, the total value was enough that she could have faced serious trouble if caught. I casually asked her about it, and she made an excuse. After she left, I talked to my daughter calmly, explaining that stealing is haram and she should encourage her friend to stop. My daughter was given some of the stolen things, and I told her to return them and let her friend know that we're aware-but also that this is a chance from Allah to make tauba and change, without involving her parents for now. Alhamdulillah, my daughter understood and felt remorseful. My husband thinks I should just keep our daughter away from her friend entirely, to avoid any awkwardness or hurt feelings with our neighbors. But I feel that suddenly cutting ties might harm our relationship, and our girls are neighbors who will naturally see each other. I want to handle this with wisdom, perhaps through my daughter or more directly, but I'm unsure. What would you advise?